











































THE 



. . . AND .... 

PRACTICAL GUIDE 


.... TO THB .... 

Examinations of the 0. S. Government Inspectors 

. . . FOR .... 

MASTERS AND MATES OF OCEAN GOING STEAMSHIPS AND 
SAILING VESSELS, AND FOR ALL INLAND GRADES 
WITH ILLUSTRATIONS 

THIRD EDITION REVISED AND ENLARGED 

.... BT ... . 

Captain W. J. Smith 

Ocean Steamship Master 

Graduate of Trinity Nautical College, Member of The National 
Geographic Society 

\ y* 

Author of “The Compass, Log, Lead and Lookout” 

7 * * 

Author of “Practical Compass Adjustment” 

Holding Master’s Unlimited Ocean and Inland License, American and 
British—Instructor in Navigation and Nautical Astronomy—Suc¬ 
cessful Adjuster of Iron and Steel Ships’ Compasses— 

Inventor of the Fogometer—Principal of The 
Seattle Navigation School. 


SEATTLE WASHINGTON, U. S. A. 


Bound, Full Cloth $3.00. 








4 




$ 




< o '% 


Copyright 

By 

CAPT. ;W. J. SMITH. 


1912 


S9 


gCI.A316978 

7^0 I 






To The American Associations of Master, Mates and Pilots 
of the United States and Territories, this Self-Instructor and 
Practical Guide is respectfully and faithfully dedicated. 



PREFACE TO FIRST AND SECOND EDITIONS. 


In placing this guide before his brother seamen, the 
author makes no attempt at any great display of originality. 
True, many of the questions contained herein are taken from his 
own chart room work book, and are from observations made per¬ 
sonally at sea (principally while in the Oriental passenger trade 
from Puget Sound ports), and worked over again with greater 
accuracy, using up-to-date nautical almanac elements; but these 
problems are, for the most part, similar to those found in other 
works. The present object is rather to put into the hands of 
aspiring mariners, a handy self-guide, to enable him with the 
aid of his epitome, or book of nautical tables, to prepare himself 
successfully to pass his examinations before the Local Inspectors 
without fear of failure, and with credit to himself as an up-to- 
date navigator. 

A sufficient number of examples are clearly worked out, or 
given as exercises, to ensure proficiency. Some are worked to 
seconds of arc, some to half minutes and others to the nearest 
minute only; and in a few cases, the shortest sea method, con¬ 
sistent with reasonable accuracy, is also shown. Nories’ Tables 
have been used almost throughout, and the numbers of the tables 
in other epitomes, corresponding to these, are given, so that the 
student may readily find and use the table he may desire. The 
answers to Examples for Practice will be found at the end of the 
guide, as also the Nautical Almanac Elements, etc., required in 
their computation. And several very useful and important 
items, not usually found in works of this kind, but very helpful 
to the navigator, have been added. 

The practical mind of a seaman naturally recoils from tedi¬ 
ous, unnecessary exactness, and for this reason the writer has 
taken great pains to render the entire work as commonplace as 
the limits of necessity and the strictness of the United States 
Inspectors will allow. The volume is based on a life studv and 



observation in all climes, and under all circumstances; at the 
same time, ideas gleaned from nautical men of repute have not 
been left out; and the simplest possible language has been used 
in explaining the various problems, and stating the rules for 
working them. 

Unavoidable errors, such as are usual in a work of this kind, 
will doubtless catch the eye, but the intelligent student will 
understand why it is next to impossible to create such a work 
absolutely perfect. Errors, however, are exceedingly few in num¬ 
ber. Should the nautical critic, or the “sea lawyer” look for 
literary gems in this work, it is needless to say that he will be 
grievously disappointed. The boy that goes to sea at fourteen, 
and remains under Neptune’s sway for thirty years, has more to 
do than work himself into a star in the literary sky. Books of 
a like kind are imported into this country and sold at a high 
figure; and, because of this, the writer endeavors, by this 
American publication, to offer to seamen the same value at least, 
at a very much reduced cost. 

In conclusion, if the young officer takes half as much 
pleasure in mastering these problems as the writer has experi¬ 
enced in working them out, he will be well paid for his studies. 
The Self-Instructor will stand or fall on its own merits. 

Seattle,, Wash., U. S. A. W. J. S. 


THIRD EDITION. 

Owing to increased demand for ‘‘ Self-Instructor ’ ’ 
this Third Edition is published, and the Author expresses 
his heartiest gratitude to the Navigator, by whose ap¬ 
preciation of the Book as a real ‘ 4 help in times of need” 
another edition has been made possible. Thanks indeed 
to the Nautical Fraternity, Self-Instructor now wears an 
additional stripe on its uniform. 

Seattle, Wash., U. S. A. July, 1912. 


W. J. S. 






f 


•l 












' 



MARINER’S COMPASS 



Easterly yar. and easterly dev. are allowed to the right, and westerly to the left in any 
quadrant of the compass. 

Easterly variation is allowed to the right and westerly to the left when reducing a 
mag. course to a true course. And dev. is allowed the same way when reducing a compass 
couise to a mag. course. 


PtS. 

X. 

X 

X 

1 

2 . 
■2J4- 

2 X- 

3 . 

SX- 
3*4 • 
3X • 

4 . 


Angles Pts. Angles 

. 2° 48' 45" 4% .47° 48' 45" 

. 5° 37' 30' .50° 37' 30" 

. 8° 26' 15" 4X .53° 26' 15" 

.11° 15' 00" 5 56° 15' 00" 

.14° 03' 45" 5% .59° 03' 45" 

.16° 52' 30" 5% .61° 52' 30" 

.19° 41' 15" 5 i/ A .64° 41' 15" 

.22° 30' 00" 6 67° 30' 00" 

.25° 18' 45" 6X .70° 18' 45" 

.28° 07' 30" 6X .73° 07' 30' 

.30° 56' 15" 6X .75° 56' 15" 

33° 45' 00" 7 78° 45' 00" 

36° 33' 45" 7X .81° 33' 45" 

39° 22' 30" 7ji.84° 22' 30' 

42° 11' 15" 7-<4 .87° 11' 15' 

45° 00' 00" 8 90° 00’ 00" 























































































LOGARITHMS. 

1. Logarithms are numbers used for shortening arithmeti¬ 
cal calculations. The word logarithms is usually contracted to 
logs. By means of logs, multiplication is converted into addi¬ 
tion, and division into substraction. 

A logarithm or log, consists of two parts separated by a 
decimal point. The part to the left is called the index, which 
we have to tell. The part to the right is called the decimal part, 
but generally, the log, and is given in Table 42 Bowditch, or 24 
Norie. 

2. To Find the Index .—The index is one less than the 
number of figures in the whole number; thus— 

The index of 56 is 1. The index of 560 is 2. The index of 
5607 is 3. The index of 56070 is 4. 

The index of 560.7 is 2. This is according to the rule, for 
though there are four figures in 560.7, there are only three in 
the whole number 560. The figures read, five hundred and 
sixty decimal seven. 

The index of 56.07 is 1; and it reads fifty-six decimal noth¬ 
ing seven. Two figures in the whole number; index 1. 

The index of 5.607 is 0. Only one figure in the whole 
number here, and by the rule, one less gives index 0. 

3. To Find the Index of a Number All Decimals. —Sub¬ 
tract the point and the number of nothings to the right of the 
point from 10. 

Thus the index of .0478 is 8; for the point 1 and 1 nothing 
make 2, and 2 from 10 leave 8. 

The index of .000721 is 6; for the point 1 and 3 nothings 
make 4, and 4 from 10 leave 6. 

The index of .726 is 9 ; for the point 1 substracted from 10 
leaves 9. The 10 that we substracted the decimal point and 
nothings from is supposed to be borrowed. 

4. To Find the Logarithm of a Number .— 

If the number consist of one or two figures the log will be 
found at the beginning of the table. Thus, the log of 48 is 
1.681241. 


6 


LOGARITHMS 


If the number consist of three figures. Seek the three fig¬ 
ures in the side column of the table, and the adjoining log 
under 0 will be the log required; thus, the log of 679 is 831870 

If the number consist of four figures. Seek the first three 
figures in the left side column, and the fourth at the top of the 
table; and abreast of the three figures under the fourth is the 
log required. Thus, the log of 4728 is 674677. 

If the number consist of five or more figures. Take out the 
log of the first four as explained above. Then from the differ¬ 
ence column on the right of the table take the difference abreast 
of the log and multiply it by the remaining figures; score off 
from the right of the product as many figures as did remain, and 
add the others to the log taken out for the first four figures. For 
instance: Find the log of 27975. The log of 279 under 7 is 
446692. The difference abreast of this is 155, which multiplied 
by 5 (the figure we could not find in the table) gives 775; score 
off one figure from the right of this, as we had but one figure to 
correct for, and we have 77 to be added to the log 446692, 
which gives us 446769, the log of 27975. Again: Find the log 
of 170908. The log of 1709, the first four figures is 232742. 
The difference is 255, which multiplied by 08, the remaining 
figures, gives 2040. Score off the two right-hand figures, be¬ 
cause there were two figures we could not take out, and there is 
left 20 to be added to the log of the first four figures, giving us 
232762, the log of 170908. The number with its index and cor¬ 
responding log should appear thus, 170908.5.232762. 

5. To Find the Number Corresponding to a Logarithm —* 

If the number be required to four figures only. Seek in the 
table for the log nearest the given one, and abreast of this in the 
left side column are the first three figures, and the fourth at the 
top of the column in which we found the nearest log. 

If the number be required to five or more figures. Find 
the log next less to the given one, this will give the first four 
figures; subtract this log (taken from the tables) from the 
given log, annex as many ciphers, one at a time, to this re¬ 
mainder as there are figures wanted above four, and divide by 


LOGARITHMS 


1 


the difference found in the right side column abreast of the log. 
Thus: Find the number corresponding to 4.478307 

The next less log gives 3008 478278 

Dividing by the diff. 145 ) 290 (2 
290 

Annexing the 2 to 3008 we have 30082, the number wanted. 
The answer must always contain one more whole number than 
the index. The above index being 4, there must be five figures 
in the whole number. 

MULTIPLICATION BY LOGARITHMS. 

6 . Take the logs of the numbers from the Table of Loga¬ 
rithms and add them together; the number corresponding to 
the sum will be the product required. 

1 . Multiply 27 by 5 by common logarithms. 

Mult. 27 log. 1.431364 

*+* 

By 5 log. 0.698970 

Answer .... 135.0 2.130334 

Here the answer must contain three whole numbers, be¬ 
cause the index is 2 . Seek 130334 among the logs. It will be 
found opposite 135 under 0. 

2 . Multiply 21.31 by 423.2 by common logarithms. 

Mult. 21.31 log. 1.328583 

-f 

By 423 . 2 log. 2.626546 

Answer .... 9018 _ 3.955129 

The index of 21.31 is 1 , because there are two whole num¬ 
bers, and the index of 423.2 is 2, because there are three whole 
numbers. Now, take out the logs. For the log of 21.31, seek 
213 in the left-hand side column, and abreast of this under 1 
is the log 328583; place it with the index 1 , as above. Seek 423 
in the left side column, and abreast of this, under 2 , is the log 
626546; place this in like manner with its index 2 . Add the 
two loss together, and seek the sum 955129 in the table. We 









8 


LOGARITHMS 


cannot find 955129 exact; then take 955110, which is the 
nearest. This is abreast of 901 under 8 . The answer is 9018, 
as there must be four figures in the whole number because the 
index is 3. 


3- Mult. 456 . 7 = 2.659631 

+ 

By 97 . 64 = 1.989628 

Answer . . 44592 4.649259 

649237 

97 ) 220 (2 
194 

26 

Here, in seeking the number corresponding to the sum of 
the logs, we find it to be 445 under 9, taking the next less log. 
Place this log under our log and subtract. Put a cipher to the 
right of the remainder and divide by the difference 97 , found 
abreast of log 649237. This gives us 2 , the fifth figure wanted 
for the whole number, because the index is 4. If we wanted 
another figure we would annex a cipher to the remainder 26 and 
divide again by the difference 97 . 

4* Mult. 2300 = 3.361728 

+ 

By . 04371 = 8.640581 
Answer . . 100 . 5 = 2.002309 


The first index here is 3, because there are four whole 
numbers. The index of .04371 is 8 , because counting the point 
1 , and 1 nothing make 2 , and following the rule, 2 from 10 leave 
8 . Find the corresponding logs, add them together and seek 
the number corresponding to this sum 002309. This gives 100 
under 5. The indices added with the logs give 12 . Subtract 10 
from this sum, because we borrowed 10 to get one of them. This 
leaves 2 for the index, giving three figures in the whole number. 

7. Rule When either of the numbers to be multiplied is 
a decimal. If the tens borrowed are paid back the answer will 








LOGARITHMS 


be a whole number. If not paid back, the answer will be a 
decimal. 

5 . Mult. . 002520 = 7.401400 Log. of 2273=356599 
“b 

By 22 . 7325 = 1.356647 Corr. for 25 =+ 48 

Answer .057 2 9=8-758047 356647 

Diff. 191 

25 

955 

382 

47-75 

The index of .002520 is 7; the point 1 , and 2 nothings, 
make 3, and 3 from 10 leave 7. The index of 22.7325 is 1 , be¬ 
cause there are two figures in the whole number. When the 
adding is done, the sum of the indices is 8 . We cannot take 10 
from this, or we cannot 'pay bach the 10 we borrowed to find the 
first index, and therefore the answer must be all decimals. 

To tell where to place the decimal point when the answer 
is all decimals. Subtract the index from 10 mentally and the 
remainder will indicate the number the first of the figures tiaken 
from the table must be after the decimal point. 

EXAMPLES. 

1 . Multiply 30 by 24.32. 

2 . Multiply 1456 by 825. 

3. Multiply 8108 by .25. 

4. Multiply .4127 by .035. 

Answers at the end of the Guide . 

DIVISION BY LOGARITHMS. 

8 . In division the logs are taken out the same as in 
multiplication. Be careful to subtract the log of the divisor 
from that of the dividend. The number corresponding to the 
remainder will be the quotient, or answer required. 

Remember the rule for taking out the logs for numbers 
having five or more figures—the first three are found in the left 
side column, and the fourth at the top. Take out the difference 









10 


LOGARITHMS 


at the right side column found abreast of the log. Multiply this 
difference by the remaining figures above four; score off from 
the right the same number of figures we are correcting for, and 
add what remains to the log of the first four figures. 

If the figures above four are ciphers, no correction is 
needed. For instance: The log of 347800 is 541330, the same 
as 3478. The number corresponding to a given log is found 
the same as in multiplication by logarithms. If required to five 
or more places of figures, seek in the tables for the log next less 
than the given log; subtract this from the given log, annex a 
cipher and divide by the difference found abreast, to the right, 
in the tables. This gives us one figure. If more are wanted, 
repeat the operation by annexing a cipher to the remainder and 
dividing again by the difference as often as necessary. 

If you find the log in the^tables exactly as required, just 
annex ciphers to the four figures found for any more figures 
needed in the answer. Thus, the number corresponding to 
6.478855 should be 3012000. Because we find the log exact 
abreast of 301 under 2, we annex three ciphers to give it seven 
places, the index being 6 . 

1 . Divide 721 by 44 by common logarithms. 

Divide 721 log. 2 . 857935 _ 

By 44 log. 1.643453 

Answer . 16.39 1.214482 

Here the decimal point is placed so as to have two figures 
in the whole number, because the index is 1 . 

2 . Divide 7246120 = 6.860105 = 860098 Diff. 60 

7 120 

By 8.94 = 0 . 951337 ““ 860105 7<200 

Answer . 81 0528 5.908768 

=== 908753 

54 ) 150 (28 
108 

420 

The first number having seven figures, must have six for 











LOGARITHMS 


11 


its index. The nearest less log corresponding to this log is 
taken out answering to the first four figures only. The differ¬ 
ence in the right-hand column is also taken out and multiplied 
by the remaining three figures, and, scoring off from the right 
of the product, also three figures, we have a 7 left, which is 
added to the log taken out. Thus the log is corrected for figures 
above four. The second line has one figure in its whole number, 
and ilts index is 0 . The log of the three figures is taken out as 
for 894. The lower is subtracted from the upper. Now find 
the number corresponding to this. The next less log being found 
and taken from our log leaves 15. The difference found in the 
right-hand column is 54. We have already taken out four 
figures of the answer, but we need six, because the index is 5. 
Annex two ciphers to the 15 and divide by the difference 54 ; 
this gives us the other two figures required. 

3 . Divide 687.4132 = 2.837218 _ 837210 

By .63421 — 9.802233 Corr. -f 8 

Answer . . 1084 3.034985 837218 

802226 
Corr. -f 7 

80223 3 


In this case the index of 687.4132 is 2 , because there are 
three figures in the whole number, and the index of .63421 is 
9 , because the decimal point with no cipher next to it counts 1 , 
and 1 from 10 leaves 9. Take the log out for 687 under 4. 
Multiply the difference 63 from the right side column by 132, 
the remaining figures; score off the three figures 316, because 
there were three remaining figures after taking out for the 
first four. Add the 8 that remains to the log of the first four, 
and you have the corrected log, .837218. Now, take out the log 
for 634 under 2 , the first four figures, which is .802226, multi¬ 
ply the difference 68 by 1 , the remaining figure, which will 
give you (after scoring off one), 7, to be added, making the cor¬ 
rected log .802233. Now subtract as in the last example, and 


63 

^32 

396 

792 

8,316 

68 

1 

6,8 











12 


SELF-INSTRUCTOR IN NAVIGATION 


you have the log 3.034985. Seek the nearest to this in the 
tables, and you find 108 under 4, and as the index is 3, the 
four figures just found are placed together, and constitute the 
answer, which in this case, is a whole number. 

9 . Rule for division by logarithms. If the first number 
is less than the second, the answer will be a decimal; but if 
the first number is greater than the second, the answer will be 
a whole number. 


EXAMPLES. 

1. Divide 1833 by 39. 

2 . Divide 629.7 by 12.6. 

3. Divide 7571200 by 17.5. 

4. Divide 3.6064 by 224. 
Answers at the end of the Guide. 


PARALLEL SAILING. 

10 . Parallel sailing is used in navigation to determine 
the value in difference of longitude of the run the ship has 
made in nautical miles east or west, called departure, while 
sailing on a parallel of latitude. 

Rule. —To the secant of the Latitude Tables 44 Bowditch, 
or 25 Norie, add the log of the Departure Table 42 Bowditch, 
or 24 Norie; the sum is the log of the difference of longitude, 
the number found in the same table. 

Always reject 10 from the index when talcing out the 
secant. Remember, too, when using the table of sines, secants, 
etc., if the degrees are at the top, the names sine, secant, etc., 
must be taken from the top and the minutes from he left side. 
If the degrees are at the bottom, the names sine, secant, etc., 
are found at the bottom and the minutes at the right side. 

EXAMPLE. 

In latitude 14° 30', the departure made good was 137 



THE DAY’S WORK 


13 


miles. Find the difference in longitude by parallel sailing. 

Lat. 14 0 30 ' Secant (— 10 ) 0.014058 , 

Dep. 137 Log. 2 . 136721 ^ 

Answer—Diff. Longitude 141.5 2.150779 

Example— Lat. 50 ° 24 Sec. 0.195572 

4 - 

Dep. 127.6 Log. 2.105851 
Answer—Diff. Longitude 200.2 2.301423 

EXAMPLES FOR PRACTICE. 

1. Lat. 36° 50', departure 48 miles; required difference 
of longitude. 

2 . Lat. 40°, departure 50.5 miles; required difference 
of longitude. 

3 . Lat. 37° 59' S., departure W. 40.75 miles; required 
difference of longitude. 

4 . Lat. 53° 28', departure 250 miles; required differ¬ 
ence of longitude. 

Don’t forgot the rule.—To the log secant of latitude add 
log of departure. The result is the log of difference of longi¬ 
tude. 

Answers at the end of the Guide. 


THE DAY’S WORK. 

The day’s work, so-called, is a means of finding a ship’s 
position at sea after sailing various courses and distances 
throughout the astronomical day, reckoning from noon till noon. 
The latitude and longitude left being known, the different 
courses steered are corrected for leeway, variation and devia¬ 
tion ; and any known current is allowed for. The direct 
course and distance the ship has made good is also ascertained 
by inspection, or middle latitude sailing. 

In correcting courses, always consider yourself at the 
center of the compass, looking toward the margin at the course 
to be corrected. 

Leeway is of course allowed from the wind. To the right, 
if on the port tack; to the left, if on the starboard tack. 









14 


THE DAY’S WORK 


Easterly variation and easterly deviation are allowed to 
the right, and westerly to the left, in any quadrant, to find the 
true course. These may be allowed together, if both are east 
or west. Or if different names, the least taken from the greater 
will leave the difference for the correction, to be allowed accord¬ 
ing to the name of the greater, easterly to the right, westerly to 
the left. It is well to have a compass card before you while 
correcting courses, such as is found ac the front of this guide. 
Leeway is usually given in points, and can easily be applied 
mentally, and the course then turned into degrees by the table 
of angles, before applying variation and deviation. If the cor¬ 
rected course exceeds 90° subtract from 180° and change its 
name from north to south, or from south to north as the case 
may be. Should the correction be larger than the course itself, 
subtract the course from the correction and change its name from 
east to west, or from west to east, as the case may be. [Never 
change both sides on one course. Courses should be so arranged 
as to read from north to easit, north to west, south to west, or 
south to east, so that in the X. E. or S. W. quadrants, correction 
allowed to the right means add, and to the left subtract; while 
in the X. W. and S. E. quadrants, correction to the right means 
subtract and to the left add. 

If the variation and deviation are given in points, let the 
courses remain in points if so given, and use Table 1 in seeking 


N 






THE DAY'S WORK 


15 


difference of latitude and departure, instead of Table 2, which 
is intended for degrees. 

The bearing of some known object may be given. This is 
reversed and called the departure course. The deviation for 
the direction of the ship’s head (usually stated), a*nd the varia¬ 
tion are then applied. This is the first course, corrected. Place 
it in the traverse tiable with its distance beside it in the proper 
column. 

The other courses are taken (without reversal) and cor¬ 
rected for leeway, variation and deviation. Place these also 
with their distances, in their proper places in the traverse table. 

The current course, if given magnetic, must be corrected 
for variation only; but if given true, it requires no correction, 
but must be placed in the traverse table as the last course, with 
its given distance beside it. 

11 . Difference of latitude and departure. Take out the 
difference of latitude and departure for the various courses and 
distances from Table 2, if degrees, or Table 1, if points, and be 
careful to give each its proper place in the traverse table, a? 
shown in the examples. Add all the eastings and westings; sub¬ 
tract the least from the greatest, naming the result departure of 
the same name as the greatest. Add up the northings and the 
southings, subtract the least from the greatest and name the 
result difference latitude, same name as the greatest. 

Note. —If a distance exceeds the limit of the table in your 
epitome, seek half the distance and multiply the result by 2 for 
latitude and departure. 

12 . Latitude In. Turn the difference latitude into de¬ 
grees (if it exceeds 60') by dividing by 60, and apply it to the 
latitude left. If both are north or both south add; if different 
names, subtract. This gives the latitude in, of the same name 
as the greater. 

13. Middle Latitude. Add together latitude left and lati¬ 
tude in, if of the same name, N. or S., and divide the sum by 2. 

The result is the middle latitude. 

Note—If they have different names, subtract the less from the 
greater and divide by 2: The result is the middle latitide, same 
name as the greater. 



16 


SELF-INSTRUCTOR IN NAVIGATION 


14. Difference of Longitude. Look for the nearest de¬ 
gree of middle latitude as a course, in Table 2, and for the de¬ 
parture, as near as possible, in a latitude column. Abreast of 
this in the distance column will be found the difference of longi¬ 
tude required; divide by 60, if it exceeds that amount. 

15. Longitude In. To the longitude left, apply the differ¬ 
ence longitude. If both are same name, east or west, add; if 
contrary names, subtract. This gives longitude in; same name 
as the greater. 

Note. —If the departure exceeds the limit of the table, seek 
half the departure and multiply the distance found by 2 for the 
difference of longitude. If the middle latitude happens to be 
less than 1°, or nothing, use the departure for the difference of 
longitude. If the longitude by adding exceeds 180° subtract 
from 360° and name the result contrary to longitude left. This 
will be longitude in. When the middle latitude exceeds 35°, the 
difference longitude should be found by parallel sailing. 

16. Course and Distance Made Good. Look for differ¬ 
ence of latitude and departure as near as they can be found to¬ 
gether in the tables. Take the course from the top of the page 
if difference of latitude is greater than departure, but from the 
bottom if departure is greatest. The distance will be found in 
its own column to the left of difference of latitude and depart¬ 
ure. Name the course same as difference of latitude and depart¬ 
ure. 

Notes. —If difference of latitude is nothing, the course 
must be east or west, same as departure; and the distance same 
number of miles as departure. If the departure is nothing, the 
course is north or south, same as difference of latitude, and the 
distance same number of miles as difference of latitude. 


THE DAY'S WORK 


17 


EXAMPLES. 



Hours 

Courses 

Knots 

Tenths 

Winds 

Leeway 

Remarks, Etc. 

Bearing ENE 

1 

SW 

6 

5 

S SE 


Cape Flattery, 

Reversed—W S W 

2 


6 

5 



in lat. 48 0 23’ 

S 6 pts W 

3 


! 6 




N, and long. 

Var. 2 pts E 

4 


6 




124 0 44’ W. 

1. S 8 pts W 

5 


6 

4 



Bearing E N 


6 


6 

6 



E magnetic. 

Pts. 

7 

WSW 

5 


South 

1 pt 

Dis. 7 miles. 

S434 w 

8 


5 





Var. 2 E 

9 


5 





2. S6^W 

10 

T T 


5 

A 





s 7 w 

JL 1 

12 


4 

4 





Var. 2 E 

I 

Exs y 2 s 

5 


sy 2 E 

^Pt 

Var. 2 points 

9 

2 


5 




easterly. 

16 

3 


5 





3. N 7 W 

4 


5 






5 


5 





S 7 E 

6 

sexs ys 

9 

5 

NW 

0 

A current set 

Var. 2 E 

7 


9 

5 



N W true 6 

4- S 5 E 

8 


10 

5 



miles. 


9 


10 

5 




S2^ E 

10 

S SE 

10 


NW 

0 


Var. 2 E 

11 


10 





5 . s y 2 e 

12 


9 





Q -> T? 









Var. 


6 . 


_E 

o = S 


Correct the courses for Variation and Leeway and 
find the ship’s position; also course and distance made 
_ good. 

7. NWtrue=N4W Note — The leeway has been allowed mentally in 
- 0 - , _ i the work before you. 

Lat. left 48 c 23’ N- J 

Lat. in 4 6 0 59’ N 
2 ) 95*^2 
Mid.lat. 47 0 4 i’ 


Dep. 50.4 = Diff. lo ng. 75* W 
i° 15’ W 


Corrected 

Courses 

Dist 

Diff 

Lat 

Dep? 

irture 

West 

7 

N 

S 

E 

W 

7.0 

S6^W 

38 

. . 

11.0 

. . 

36.4 

N 7 W 

28 

5-5 



27-5 

S 5 E 

25 


13 9 

20.8 


s ke 

40 

.. 

39-8 

3 9 


South 

29 


29.0 

. . 

.. 

N 4 W 

6 

4-2 


1 .; 

4-2 


9-7 93-7 
9-7 


24-7 75 -i 

24.7 


Diff. Lat. 60 | 84. o Dep.50.4W 


Course S 31* W; Distance 98 m iles 


Lat. left 
Lat. in 


i c 24 ’ S 
48 23 N 
46° 59’ North 


Long, left 124° 44’ W 
Diff. long. 1 15 W 

Long, in 125 0 59’ W 

































































18 


THE DAY’S WORK 



Hour 

Courses 

| Knots 

| Tenths 

Wind 

Leeway 

Dev. 

1 

j Remarks, etc. 

S 2^ E=S 28° 

E 

1 

S S E 

6 

i 5 

SW 

Xpt 

3 °W 


Error 19 0 

E 

2 


6 

5 




Lat. left 

1. S 9 0 

E 

3 


6 





46° io’ N 

S 5 E=S56°” 

E 

4 


6 






Error 17 

E 

5 


6 





Long, left 

2. S 39 

E 

6 

S E 

5 


S SW 

1 

5 °W 

125 0 14’ W 


-— 

7 


5 

4 




i 

S 3 X E=S 39 * 

E 

8 


5 

6 





Error 18 

E 

9 


5 






3- S 21 

E 

10 

SEXS 

6 


swxs 

H 

4°Wi 




11 


6 





Var. 22 0 E 

s 3X W=s 42 q 

W 

12 


6 

5 





Error 26 

E 

1 


7 

5 





4. S 68 

W 

2 


7 








3 

SW ^ S 

7 I 


sexs ys 

X 

4 °E 


S 2% W=S 25 0 

W 

4 


7 






Error 24 

E 

5 


8! 






5 - S49 

W 

6 


8| 








7 


5 






N 6 W=N 67° 

W 

8! 

sxw^ W 

5 


SEKS 

X 

2 c E ! 


Error 22 

E 

9 


5 



i 


Current W NW 

6. N45 

W 

10 


5 





Magnetic 



11 


5 





12 miles 



12 


4 







The courses are corrected mentally for leeway and then turned into 
degrees. The variations and deviations are added together when of same 
name, and the least subtracted from the greatest when of different names; 
the result is the error, and is named the same as the greater and applied 
accordingly, 


Latitude, left, 46° 10’ N 
Latitude, in 44 32 N 
2) 90 42 
Mid. latitude 45 21 


True 

Course 

Dists. 

DIFF. DAT. 

DEPARTURE 

N 

S 

E 

W 

S 9 0 E 

S 39 E 
S 21 E 
S 68 W 
S49 W 
N 45 W 

31 

21 

33 

35 

24 

12 

8.5 

30.6 

16.3 

3 °-8 

13.1 

15.7 

4-8 
I3.2 
11.8 

32.5 

18.1 

8-5 


Dep. 29.3=diflf. Long. 41’ W 8.5 106.5 29.8 59.1 

8.5 29.8 

Diflf. lat. 60)98.0 De p. 29.3 W=4i 

- 

Lat. left 46 10 N 
Lat. in 44° 32’ North 

Long, left 125 0 14’ W 
DifF. long. 41’ W 
Long, in 125° 5 5’ West 


Course made good, S 17 0 W 
Distance, 103 miles. 











































































SELF-INSTRUCTOR IN NAVIGATION 


19 


Bearing S^E revrs’d 
=Nj£w=N 6°W 

Var. 


15 E 


1. 


2. 


4 . 


6 . 


Dev. 


Var. 


Dev. 


Var. 


Dev. 


Var. 


Dev. 


Var. 


Dev. 


Var. 


Dev. 


Var. 


Dev. 


Var. 


N 

9 

E 


4 

W 

N 

5 

E 

N 

37 ° 

E 


15 

E 

N 

52 

E 


4 

W 

N 

48 

E 

N 

5 i° 

E 


15 

E 


66 



5 

W 

N 

61 

JE 

N 

34 ° W 


15 

E 


19 



6 

E 

N 

13 

W 

N 

48 °W 


15 

E 


33 



5 

E 

N 

28 

W 

S 

79 c 

E 


15 

E 


64 



8 

W 

S 

72 

E 

N 

73 ° 

E 


15 

E 


88 



9 

W 

N 

79 

E 

N 

23°W 


15 

E 

~N 

8 

W 


| Hours 

Courses 

| Knots 1 

| Tenths | 

Wind 

Leeway 

Dev 

Remarks, Etc. 

1 

NEXN 

7 


NWXN 

Xpt 

4 °W 

A point in lat. 

2 


7 





19 0 15’ North 

3 


6 





long. 167*45’ 

4 


6 





E, bearing by 

5 

NE 

7 

2 

N NW 

Kpt 

5 °W 

comp. S. % 

6 


7 

4 




E, distant 10 

7 


7 

4 




miles; ship’s 

8 


8 





headNEXN. 

9 

nwxn 

7 

5 

WXS 

0 

6°E 

Dev. as per 

10 


7 

5 




log 4 0 W. 

11 


8 






12 


8 






1 

NWXW 

7 

5 

SWXVV 

,Vpt 

5 °E 

Var. 15 0 E 

2 


7 

5 





; 3 


8 






4 


6 






5 

East 

7 

6 

N NE 

I 

8°W 

A current set 

6 


7 

4 




N NW 

: 7 


7 






8 


7 






; 9 

ENE 

6 

4 

North 

'Avt 

9 °W 

Correct mag. 

10 


6 

4 




36 miles. 

11 


6 

6 





12 


6 

6 






Correct the courses mentally for leeway and con¬ 
vert into degrees. The var. and dev. are here 
allowed separately. The first correction for the first 
course is more than the course, so we subt. the 
course from the correction and change the name of 
the course to East. 


True 

Course 


N 5 C 
N 48 
N 61 
N 13 
N 28 
S 72 
N 79 
N 8 


E 

E 

E 

W 

W 

E 

E 

W 


Dists. 


DIFF. DAT. 

DEPARTURE 

N 

S 

E 

W 


10 

26 

30 

3 1 
29 
29 
26 
36 


10. o 
17-4 

14.5 
30.2 

25.6 


50 

35-6 


9.0 


0.9 

19-3 

26.2 


27.6 

25-5 


7.0 

136 


5 0 


Diff. Eat. 60 



9.0 


99-5 

25.6 


25.6 


Dep. 73.9 E= 6,o )7 ( 9 


Course made good N 30° E. 
Distance 149 miles. 


2°o9’ N 
Eat. l eft 19 15 N 

Eat. in_2i°24’ N 

2) 4 °° 39 ' 


i q I9’E 

Eong. left 167 45 E 
Eong. in 169*04’ E 


20 19 


Mid. lat. 





















































































20 SELF-INSTRUCTOR IN NAVIGATION 


EXAMPLE FOR PRACTICE—No. i 



Cfl 

t-. 

3 

O 

Courses 

-M 

O 

O 

5 

a 

<u 

Wind 

cd 

£ 

<L> 

V 

Remarks, etc. 


w 


w 

H 


►4 



I 

N NE 

4 

7 

East 

ipt. 



2 


4 






3 


4 

3 



A point in 


4 


4 




Lat. 38° 16’ N 


5 

NXE 

4 


EXN 

X 

Long. 15 0 14’ E 

Correct the courses 

6 


4 

7 



Bearing South 

for Variation and 

7 


4 

8 



Mag.; Dist. 6 

Leeway, and find 

1 8 

1 9 

sw 

4 

5 

5 

6 

SSE 

2 

miles. 

Latitude and Lon¬ 

10 


5 

4 



i 

gitude in; also the 

11 


5 

7 




course and dis¬ 

12 

w sw 

5 

3 

South 

I X 

Var. 2 pts. W. 

tance made good 

1 

2 

6 

6 

6 

2 

by Inspection. 

3 


6 






4 


6 

2 





5 

West 

6 

6 

N NW 

I 



6 


6 

7 





7 


6 

8 





8 


5 

9 





9 

South 

6 

7 

w SW 

X 

Current set 


10 


6 

8 



N NW Mag. 


11 


7 

1 



28 miles 


12 


7 

4 





EXAMPLE FOR PRACTICE—No. 2 



cn 
u 
3 

Courses 

(A 

*-> 

0 

3 

CA 

35 

4 -) 

3 

<u 

Wind 

oa 

£ 

<v 

.2 

V 

Remarks, etc. 


w| 


w 

H 



Q 



11 

nwxn 

7 

3 

NEXN 

Xpt 

o° ! 

A point in 


2 ! 


7 

4 



Lat. 40° 20’ N 


3 


7 

3 




Long.i25°2o’w 


4 


7 

6 




bearing by 

Correct the courses 

5 

NW 

7 

N NE 

I 

3° E 

Compass 

for Leeway, Vari- 
tion and Devia¬ 

6 

7 

8 


7 

7 

8 

7 

4 

3 




EXN XN 

Ship’s head 

nwxn 

tion, and find Lat¬ 

9 

W NW 

8 

5 

North 

X 

ii° E 

Deviation as 

itude and Longi¬ 

10 


8 

5 




per log o° 

tude; also true 

11 


8 





Dist. 5 miles 

12 


8 





Var. 16® E. 

course and dis¬ 

1 

NWXW 

8 


NXE 

X 

1 7° E 

tance made good 

2 


8 




Current NW 

by Inspection. 

3 

A 


8 

7 

3 

A 




Mag. 30 miles 


5 

sxw 

7 

6 

sexe 

0 

14 0 E 



6 


7 

7 






7 


7 

! 4 






8 


7 

i 6 






9 

s sw 

7 

1 4 

SE 

X 

23 0 E 



10 


7 

2 





11 


7 4 






12 


7 j 
















































SUN’S MERIDIAN ALTITUDE 


21 


EXAMPLE FOR PRACTICE—No. 3 











ours 

Courses 

05 

O 

O 

JS 

s 

Wind 

a! 

£ 

<U 

Remarks, etc. 


£ 


w 

H 


►3 



1 

NXE 

6 

5 

NWXW 

ipt 



2 


6 

5 





3 


6 




A point in 


4 


6 




Lat. 50° 29’ S. 


5 

North 

6 


W NW 

X 

Long. 59° 20’ W 

Correct the courses 

6 

7 


6 

7 




Bearing WXS 
Magnetic; 

for Leeway and 

8 


7 




Distance 

Variation, and 

9 

N NW 

8 


West 

1 

12 miles 

find ship’s posi¬ 

10 


8 

g 

c. 




tion ; also course 

11 

12 


8 

O 

A 




and distance made 

1 

EXS 

7 

4 

6 

nrxn 

iX 

Var. 2 pts. E. 

good. 

2 


7 

6 





3 


7 

4 



No deviation. 


4 


7 

4 





5 

SE 

7 


E NE 

1 

Current set 


6 


7 




North correct 


7 


6 




Mag. 24 miles 


8 


6 






9 

SW 

6 


S SE 

IX 



10 


6 






11 


5 






12 


5 






Answers at the end of the Guide. 


ALTITUDE BY SUN'S MERIDIAN 
ALTITUDE. 

The sun’s declination should be corrected for the approxi¬ 
mate longitude of the ship by Table 21, Norie, or other table for 
that purpose. If this is not done, the declination must be cor¬ 
rected by the variation in 1 hour for the hours and tenths of an 
hour of the Greenwich date, for, remember, the declination, like 
other Xautical Almanac data, is given for noon at Greenwich. 

17. To Find the Greenwich Time. Put down the date 
and Oh 0 m Os. This is apparent noon at ship. Turn the 
longitude into time by multiplying by 4 and dividing by 60 ; or 
use Table 7, Bowditch, or 19 Norie. If west longitude add to 
apparent time at ship; but if east, subtract from apparent time 
at ship. We now have apparent time at Greenwich. When 
the longitude in time is east to be subtracted, borrow 24 hours 
and call the date one day less. 
















22 


SELF-INSTRUCTOR IN NAVIGATION 


18. Correct the Declination. Take out the declination 
and the variation in 1 hour from page 1 of the month, Nautical 
Almanac, for the Greenwich date. Multiply the hourly varia¬ 
tion by the hours and tenths of an hour in the Greenwich time, 
and the result is the correction for the declination, to be added 
if declination is increasing, but subtracted if declination is de¬ 
creasing. 

It is best to take out declination for nearest noon and 
work the corrections backwards, as in the following example, 
where the hours exceed 12. 

EXAMPLE. 


d. h. ni. s. 
A. T. Green. Aug. 7 19 44 12 

24 

Time from Noon 4 15 48 


Decl. N. Deer. Var. in 1 hour. 
Aug. 8 i 6 u 12’ 47 ’’ 42 ”.45 

Corr. + 33 _ +3 

Decl. 16 15 50 N. 12735 

^980 
6,o ) 18 ,2^535 
3 03 


Note .—In the above example, although the declination is 
decreasing, the correction is added because we are working back 
from nearest noon. The tenths of an hour are found bv divid¬ 
ing the minutes by 6. After multiplying variation in 1 hour 
by the hours and tenths, score off from the right as many figures 
as there are decimals, and divide the rest by 60 to reduce them 
to minutes, if necessary. When declination for Greenwich day 
'and day following have different names, call the declination de¬ 
creasing, and the correction subtractive. If the correction is less 
than the declination, subtract the correction from the declina¬ 
tion, and give the result same name as the declination; but il 
the correction is greater than the declination subtract the declin¬ 
ation from the correction and name contrary to the declination. 

19. Find True Altitude. To the observed altitude apply 
index error, if any; addif + ; subtract if—; dip for height of 
eye, found in Table of Dip, always subtract (14 Bowditch; 5 
Norie) ; sun’s correction (refraction and parallax) Table 18 
Norie, always subtract ; sun’s semi-diameter from page 2 Nau¬ 
tical Almanac, for the day given in the example; lower limb 
add, upper limb subtract. The result is the true altitude. 









SUN’S MERIDIAN ALTITUDE 


23 


20. Zenith Distance. Subtract the true altitude from 
00° 0' 0", and name the result zenith distance, contrary to the 
bearing of the sun as given in the example. 

Mote: If the true altitude exceeds 90deg., subtract 90deg. and 

name the result Zenith Distance same name as sun’s bearing. 

21. Find the Latitude. Under the zenith distance place 
the sun’s corrected declination, with its name N. or S.; add 
these two together if of the same name; subtract if different 
names. We now have the latitude, always of the same name as 
the greater. 

Note .—Table 9, Norrie, gives one correction for an altitude 
of the sun’s lower limb, including dip, refraction, parallax and 
sun’s semi-diameter. The result is very close to the truth, 
though it may differ a few seconds of arc from the above more 
elaborate method of using many tables. 


EXAMPLE 1. 

1900. June 3rd; longitude 140° W.; observed meridian 
altitude of the sun’s lower limb 60° 13' 30" bearing S.; index 
error + O' 30" ; height of eye 28 feet. Required the latitude. 


Green. Time, 
d. h. m. s. 
A. T. S. June 3000 
Long, in Time 4 - 9 . 20. o 


Long. 
W 


140 

4 


Decl. N. Incr. 
d. 

June 3 22° 17’44” 

Corr. -f 2 54 


Var. in 1 Hour. 


18”.7 
9 -3 


A. T. Green. 3d 9 20 


6,0)56.o Corr. Decl. 3d 22.20.38 N 
0 9 h. 20 m 


56r 

1683 


6 ( o ) I7.3-9 I 
2’ 54” 


Obs. Alt. 

I. Error 

6o° 13’ 30” S. 

+ 30 

SHORT 

method. 

Dip 

60 .14 .00 

Alt. 

60° 13’ 30” 

— 5 11 

I. E. 

+ 30 

Sun’s Corr. 

60 08 49 
— 29 

Table 9 Norie 

60 .14 .00 
+ 10 .00 


60 08 20 

True Alt. 

60 .24 .00 

Semidia. 

+ 15 47 


90 0 0 

True Alt. 

60 24 07 S. 

Z. Dist. 

29 36 0 


90 00 00 

Decl. 

22 20 38 

Zen. Dist. 

29 35 53 N. 

Latitude 

5 i *5b .38 

Corr. Decl. 

22 20 38 N. 



Latitude 

5 i° 56 ’ 3 i” N. 




Note .—The difference is but 7 seconds of arc. The style is 
all right, and is used every day at sea on ocean greyhounds. 



























24 


SELF-INSTRUCTOR IN NAVIGATION 


EXAMPLE 2. 

1900, January 29 th; longitude 173° 05' E; observed me¬ 
ridian altitude sun’s upper limb 22° 48' 40" bearing S; index 
error — 1 ' 20 " ; eye 26 feet. Required the latitude. 


d. h. m. s. Long. E Decl. S. Deer. H. Var. 

A. T. S. Jan. 29 o o o 173 0 5’ Decl. 18 0 14’ 13” S 39”.5 

_ __4 

Long, in Time—11 32 20 6,0)69,2.20 Corr. — 8^4 12 5 

A. T. Green. 28.12.27.40 11.32.20 C. Dec 18.05 59 S 1975 

========== -— 4740 


^p)49<3^75 

8 ’ 14 ” 


The declination is taken out for the 28th, and corrected by 
its hourly variation for 12 hours and 5 tenths. The longitude in 
time here is subtracted from ship’s time because the longitude is 
east. 

Obs. Alt. 22 0 48 ' 40 " S. 


I. E. — 1 20 

22 .47 .20 

Pip- “_5_ 

22 .42 .20 

Corr. T. 18 Norie. — 2 8 

22 . 40.12 

Semi. dia. U. L. — 16 .16 

True Alt. 22 .23 .56 S. 

90 o o 

Zen. Dist. 67 .36 .04 N. 

Corr. Decl. 18 .5 .59 S. 

Latitude 49 .30 .05 North. 


The semi-diameter in this case lias been subtracted, be¬ 
cause the sun’s upper limb was observed. 

EXAMPLE 3. 

1900, April 11 th; longitude 48° W.; observed meridian 
altitude sun’s lower limb 38° 5' 35" bearing N.; eye 21 feet; 
index error 4-1' 26". Required the latitude. 



















bUN’S MERIDIAN ALTITUDE 


25 


h. m. s. 
o o o 

3 !2 o 

Decl. N. Incr. 
48° \V 80 15’ 11” 

4 2 56 

H Var. 
55’M 

3 *2 

h. m. s. 

3 12 o 

6,0)19,2 Cor. Del.8° 18’ 07” N 
3 12 

IIO 2 

1653 



6,0)17,6.32 
2 ( 56” 

Obs. Alt. 

I. E. 

38° 5'35"N. 

+ 1 26 


Corr. T. 9 

38.07.OI 

Norie. + 10 .21 


T. Alt. 

38.17 .22 N. 

90 0 0 


Z. Dist. 
Decl. 

51 .42 .38 s. 

8 18 7 N. 


Latitude 

43 . 24.31 South. 



One correction from Table 9 Xorie has been used in cor¬ 
recting this altitude. 

EXAMPLES FOR PRACTICE. 

1. 1900, February 27th; longitude 150° 45' E.; observed 
meridian altitude sun’s lower limb 50° 6' 35" X.; eye 24 feet; 
index error — 1' 40". Required the latitude. 

2. 1900, January 17th; longitude 127° 40' W; observed 
meridian altitude sun’s upper limb 50° 35' 35" X.; eye 28 feet; 
index error — 1' 30". Find the latitude. 

3. 1900, August 7th; longitude 36° E.; observed meri¬ 
dian altitude sun’s lower limb was 62° 34' 55" S.; eye 25 feet; 
index error +25". Required the latitude. 

4. 1900, June 4th; longitude 178° 50' W.; observed 
meridian altitude sun’s lower limb 69° 20' 45" X.; eye 29 feet; 
index error — 1' 7". Required the latitude. 

5. 1900, October 13th; longitude 114° 59' E.; observed 
meridian altitude sun’s lower limb 61° 9' 45" S.; eye 24 feet; 
index error — 2' 10". Required the latitude. 

Answers at the end of the Guide . 


















MERCATOR’S SAILING. 


This is a method of finding the true course and distance 
between any two places, A and B, by calculation on Mercator s 
principle. 

22. To Find Difference of Latitude. If latitudes are 
different names, add them together; but if the same name, sub¬ 
tract the less from the greater, and bring the result to miles by 
multiplying the degrees by 60 and adding in the minutes. Call 
this difference of latitude north or south, as the place bound to 
is north or south of the place from. 

23. Meridional Difference of Latitude. Take out meri¬ 
dional parts for both latitudes from Table 3 Bowditchor Norie; 
degrees at the top, minutes at the side of table. Latitudes dif¬ 
ferent names, add the meridional parts; latitudes same name, 
subtract the least from the greatest, and name the result meri¬ 
dional difference latitude. 

24. Difference of Longitude. Longitudes contrary names, 
add them together; longitudes same name, subtract the least 
from the greatest. Turn the result into miles by multiplying 
the degrees by 60 and adding in the minutes. Name this differ¬ 
ence of longitude, east or west, as the place to is east or west of 
the place from. 

When, with longitudes contrary names, the sum exceeds 
180°, subtract from 360°, then reduce to miles; but in this case 
name it difference of longitude east or west, same as longitude 
left. 

25. To Find the Course. From log difference of longi¬ 
tude, Table 42 Bowditch, or Table 24 Norie, subtract log meri¬ 
dional difference of latitude, same table, and look up the tangent 

of the remainder in Table 44 Bowditch, or Table 25 Norie. 
This is the course, to be named according to the difference of 
latitude and difference of longitude. Always add 10 to the 
index of the log of difference of longitude. 

26. To Find the Distance. To the log secant of the 
course (same table as the tangent) add log difference of lati- 


MERCATOR 


27 


tude, Table 42 Bowditch, or 24 Xorie, and take out the number 
corresponding to their sum from the same table. This will be the 
distance. Always substract 10 from the index of the secant of 
the course. 

Always name the course according as the ship is making 
northing or southing, and easting or westing; express the course 
in degrees and minutes. 

Note. —When the sum of longitudes contrary names has 
been taken from 360°, name the course same as longitude left. 

EXAMPLE. 

Required the course and distance from Cape Flattery, in 
latitude 48° 23' X. and longitude 124° 44' W., to the eastern 
extreme of Oahu island, near Honolulu, in latitude 21° 18' X. 
and longitude 157° 39' W. 

C. Flattery Lat. 48° 23’N. Mer. Pts.3309 Long.124 0 44’W. 

Oahu Is. Lat.. . 21 18 N. Mer. Pts. 1300 Long. 157 39 W. 

27 .5 Mer. Diff. Lat. 2009 32 .55 

60 : - : 60 

Diff. Lat. 1625 South. Diff. Long. 1975 West. 

For the Course. For the Distance. 

Diff. Long. 1975 Log. + 10=13.29557 Course, 44 0 3 I, Secant—10=0.14688 

Mer. Dif. Lt. 2009 Log. = 3.3029 8 Dif. Lt. 1625 Log. =3.21085 

Course S. 44 ° 3 i ’ W. Tang. = 9.99259 Distance, 2,279 Miles, = 3-35773 

Course S. 44° 31' 00" W.; distance 2,279 miles. 
EXAMPLE. 

Find the course and distance from Cape Bealle, in Lat. 48° 
48' X. and Long. 125° 14' W., to a position off Unimak Pass, in 
Lat. 53° 40' X. and Long. 164° 0' W. 

Cape Bealle, Lat.. . 48°48’ N. Mer. Pts.3364 Long.I25°i4’ W. 

Unimak Pass, Lat. 53.40 N. Mer. Pts. 3 8 3 ^ Long. 164 .0 W. 

4.52 Mer. Diff. Lat. 467 38.46 

60 - 60 

Diff. Lat. 292 North. Diff. Long. 2326 West 

For the Course. For the Distance. 

Diff. Long. 2326 Log. +10=13.366610 Course, 78 ° 39 ’ Sec. —10=0.705971 

Mr.Dif.Lat. 467 Log. = 2.669317 Diff. Lat. 292 =2,4653 83 

Course N. 78°39 > W. Tang ^io.697293 Distance, 1484 miles, =3 171354 

Course X. 78° 39' W.; distance 1,484 miles. 





























28 


SELF-INSTRUCTOR IN NAVIGATION 


Note .—Tables 3 in Bowditch and Norie do not give exactly 
the same meridional parts, and as these Mercators are worked 
from Norie, some difference will be found if Bowditch is used. 
The first example is worked by Bowditch. 

EXAMPLE. 

Required the true course and distance from Sierra Leone 
to Cape Branco by calculation on Mercator’s principle. 

Lat. Sierra Leone, 8° 31* N. Mer. Pts 513 Long.13 0 16’ W. 

Lat. C. Branco . . . J_ _.8 S. Mer. Pts 429 Long. 34 .48 W. 

15 .39 Mer. Diff. Lat. 942 21 .32 

60 - 60 

Diff. Long. 939 South. Diff. Long. 1292 West. 

Diff. Long... .1292 .13.111262 Course, 53 0 54’^ .0.229827 

Mer. Diff. Lat.. 942 .2.974051 Diff. Lat.939 .2972666 

Course S. 53 0 54’>£ W. 10.137211 Dist. 1594 miles, .3.202493 

EXAMPLE. 


Required the true course and distance from Otago to Cal¬ 
lao by calculation on Mercator’s principle. 

Lat. Otago.45° 46’ S. Mer. Pts.3095 Long.170° 38’ E. 

Lat. Callao. 12 .4 S. Mer. Pts. 729 Long. 77 .5 w. 

33 .42 N. Mer. Diff. Lat. 2366 247 .43 

60 360 .00 

Diff. Lat.2022 Miles. 112 .17 E. 

60 

Diff. Long- 6737 Miles. 

Diff. Long. 6737.13.828467 Course 70° 39’.0.479729 

Mer. Diff. Lat. 2366, .3.374015 Diff. Lat. 2022.3*305781^ 

Course N. 70° 3 9* E. . 10.45445 2 Distance 6102 miles, .3.785510 


EXAMPLES FOR PRACTICE. 

1. Find true course and distance from A to B. Lat. A, 
36° 35 S.; Long., 34° 35' W. Lat. B, 48° 49' S.; Long., 
30° 11' W. 

2. Required true course and distance from A to B. Lat. 
A, 9° 36' N.; Long., 20° 36' W. Lat. B, 13° 36' S., Long. 
7° 56' E. 

3. Find true course and distance from A to B. Lat. A, 






























AMPLITUDE 


29 


13° IT 1ST.; Long., 59° 24' W. Lat. B, 8° 48' S.: Long., 
13° 14' E. 

4. Required true course and distance from A to B. Lat. 
A, 42° 51' K; Long., 124° 30' W. Lat. B, 52° 68 ' K; Long., 
172° IT E. 

Answers at the end of the Guide . 


AMPLITUDE. 

Compass Error and Deviation by Sun's Amplitude. 

The apparent time at ship, latitude, longitude east or west, 
the observed compass amplitude, and the variation are usually 
given in the question. 

If apparent time at ship is P. M., write down the date and 
time as given; but if apparent time at ship is A. M., add 12 
to the hours and call the date one day less. 

Find the Greenwich Time. To the apparent time at ship, 
as now stated, apply the longitude in time; west longitude, add; 
east longitude, subtract; the result is apparent time at Green¬ 
wich. 

Notes. —The longitude is turned into time by multiplying 
by 4 and dividing by 60; or we may use Table 7 Bowditch or 19 
Norie, for this purpose. When the longitude in time west, 
added to apparent time at ship exceeds 24 hours, subtract 24 
hours and call the date one day more. When the longitude in 
time east, to be subtracted, is greater than the hours, minutes 
and seconds of the apparent time at ship, add 24 hours to the 
apparent time at ship and make the date one day less. 

Declination for the Greenwich Time. Take out the decli¬ 
nation from page 1 of the month for the Greenwich day, also 
the variation in 1 hour, found beside the declination. Multiply 
this hourly variation by the hours and tenths of an hour of the 
Greenwich time, and we have the correction for the declination, 
to be added if the declination is increasing, and subtracted if 
the declination is decreasing. Thus we have the declination 
corrected for the Greenwich time. 



30 


SELF-INSTRUCTOR IN NAVIGATION 


Note.—When the declination on the following day is of a 
different name f the declination is decreasing . In ihis case, if 
the correction to be subtracted is greater than the declination, 
subtract the declination from the correction and name the result 
contrary to the declination. If the correction is less than the 
declination, subtract the correction from the declination and 
name the result corrected declination, the same name, north or 
south, as the declination. 

27. Find the True Amplitude. To the log secant of the 
latitude (10 subtracted from the index), add the log sine of 
the corrected declination; the result will be the log sine of the 
true amplitude. 

All the logs are found in Table 44 Bowditch or 25 Norie. 

28. Name the True Amplitude. Name it from east if 
A. M., from west if P. M. at ship; towards north or south, ac¬ 
cording as corrected declination is north or south. 

29. Error of the Compass. Right under the true ampli¬ 
tude as found, place the compass amplitude given in the ques¬ 
tion. If both are north or south subtract the least from the 
greatest; but if contrary names, add them together. The re¬ 
sult is the error. 

Notes. —If the compass amplitude ns given in the example 
is not reckoned from the same point east or west as the true, 
subtract the compass amplitude from 180° and change it to 
east or west, the same as the true amplitude. Do not neglect 
this, for both amplitudes must be reckoned from the same point 
east or west. If the declination is 0° 0' the true amplitude is 
E. 0° 0' if A. M. and W. 0° 0' if P. M. If the latitude is 
0° 0' the true amplitude is the same as the declination. 

30. Name the Error. Consider yourself at the center of 
the compass looking toward the point east or west from which 
the amplitudes are reckoned. Now, if the true is to the right of 
the compass amplitude, the error is east; but if the true is to 
the left, the error is west. 

31. To Find the Deviation. Place the variation given in 
the example under the compass error, and if they are both east 
or both west, subtract the least from the greatest; but if con- 


AMPLITUDE 


31 


trary names, add them together. The result is the deviation. 

32. Name the Deviation. When error and variation have 
contrary names, name the deviation same as the error. When 
error and variation have same name, name the deviation same as 
the error if the error is greatest; but contrary to the error if the 
variation is greatest. Commit this rule to memory. It will 
save you much worry. 

Notes. —If the error is 0°, the deviation will be the same 
as the variation, but of a contrary name. If the variation is 0°, 
the deviation is same as the error and of the same name. 


EXAMPLE 1. 


1900, October 7th 7 h 10 m P. M. apparent time at ship; 
latitude 40° 29'; longitude 37° W.; sun’s compass amplitude, 
W. 14° 21' S. Required the compass error. 


A. T. S. 7d 7 h iom 

Long, in T....-j- 2 28 

A. T. G. 7 -9 -38 


Long. 37 0 \V. Decl. S. increasing 

_4_ 5° 25* 49” 

6,0)14,8 Corr . -(- 9 .12 

- Corr. decl. 5 .35 .01 S 

2h 28m 1 ■ • ■ 1 


Hourly Var 

57”. 5 
9 -6 


3450 
_5175 

6,0) 55,2.00 

9 * 12” 


Lat. 40° 29’ Secant—10 = 0.118847-1- 

Corr. Decl.-. 5° 35’ Sine 8.988083 


True Amp. W 7 0 21’ S 9.106930 L 

Comp. Amp. W14 2i* S 

Error. 7°oo’ East c 


In the above example no variation is given, so that no devi¬ 
ation is called for. The true amplitude is west, because it is P. 
M., and south, because the corrected declination is south. The 
least amplitude is subtracted from the greatest, because they 
are the same name, both south. The error is named east , be¬ 
cause the true amplitude is to the right of the compass ampli¬ 
tude, when looking towards them from the center of the com¬ 
pass. 

EXAMPLE 2. 

1900, March 9th 5 h 20 m 19 s A. M. apparent time at 
ship; Lat. 39° 40'; Long. 150° 12' E.; sun’s compass ampli- 




























82 


SELF-INSTKUCTOlt IN NAVIGATION 


tude E. 2° 45 ' S.; 

variation 3 ° 

10 ' W. Required the error of 

compass and the deviation. 



A. T. S. 8d i7h 20m 19s 

Long. in T... — 10 .00 .48 

Long. I50°i2’ 

East Decl. S. decreasing. 

4 ° 56 ’ 50” 

H. Var. 
58”.45 

A. T. G. 8d 7 .19 .31 

6,o) 60,0.48 

Corr. — 7 .07 

7-3 


10 .00 .48 

Corr. decl. 4 .49 .43 S 

17535 

40915 




6,0) 42,6.685 

Lat.. 

> 

7 * - 7 ” 

V 

Corr. Decl.. 


True Amp.. 


S. =9.038499 w - a- - 

t 

Comp. Amp.. 


S. 


Error.. 

Var. 


E. 

W. 


Deviation.. 


r 


This example is worked out to nearest half minute of 
are, as near as the examination calls for. The time being A. M.. 
12 is added, to the hours and the date made one day less. The 
longitude in time is subtracted from apparent time at ship, be¬ 
cause it is east. The true amplitude is reckoned from east be¬ 
cause it is A. M. Towards south because the corrected declina¬ 
tion is south. The least amplitude is subtracted from the 
greatest because they are same name, south. The error is 
named E., because the true amplitude is to the right of the 
compass amplitude. The error and variation are added because 
they are different names, east and west. The deviation is named 
east like the error, because the error and variation have contrary 
names. 

Note .—The name of the deviation 
can also be found by marking off the 
error and variation at the north point 
of the compass, thus— 

E. representing error and V. the variation. Easterly error is 
marked off to the east of N. and westerly variation is marked 
off to the west of N., shown by the adjoining compass. Now. 
the error being to the right of the variation the deviation is east. 
If the errror had been to the left of the variation, the deviation 
would have been west. 

EXAMPLE 3. 

1900, July 3rd, 3h 20 m 35 s A. M., apparent time at 
6hip; Lat. 49° 49'; Long. 167° 15' W.: sun’s compass ampli- 



































AMPLITUDE 


33 


tude IT. E. | E.; variation 12 ° 50' E. Find the error and 
deviation. 


A. T. S-.2d 15I1 20m 

Don g inT. ii 9 
A. T. G.^. 3d .2 .29 


35 * 

^35 


Eat-45*49’ Sec. 0.190282 

Decl—22 59 Sia. 9.591580 "*" 

T. Amp....H 37 ®i 4 ^ N.= 9.781862 
C. Amp.... N. 


Error. 2.08 E. 

Var. 12.50 E • 

Dev. io®42’ W. 


Decl. N. decreasing 
Dong, i67°I5’ W 22°59’24” 

_ 4 Cor r. — 30 

6,0)66,9.0 0 Corr. Dec. .22.58.54 N . 

11 li 09 m 



[. Var. 
ii w .86 
_ ^5 

5930 

23I2 

29.650 


l 


Here again, the time being A. M., 12 is added to the hours 
and the date put back one day. The longitude in time, west, 
added, makes it exceed 24 hours, so we reject 24 and call the 
date one day more. The true amplitude is E., because the 
time is A. M., and H., because the corrected declination is 
north. The compass amplitude N. E. \ E. = E. 3^ points. 
H.= E. 39° 22' 30" JST. The error is E., because the true ampli¬ 
tude is to the right of the compass amplitude. The deviation is 
W., because the error is to the left of the variation; or, using 
the other rule, because the error and variation have the same 
name, but the variation is greater than the error. 


EXAMPLE 4. 


1900, September 20th, 6 h 0 m 0 s P. M., apparent time at 
ship; Lat. 23° 15'; Long. 146° 05' E.; sun’s compass ampli¬ 
tude W. \ X.; variation 10° 55' E. Required error and devia¬ 
tion. 


A. T. S.2od 6h om os 

Dong, in T. — 9 .44 .20 

A. T. G.I9d 20 .15 .40 

24 


T. from Noon 2od 3 .44 .20 


Lat. 

23 ° 

15 ’ 

Sec. 0.036783 , 

Decl.... 

1 

14 

Sin. 8.332924' 1 

T. Amp. W. 

i° 

*o*N\ Sin. 8.369707 

C. Amp. W. 

2 

48 

45 N. 

Error. 

1 

28 

45 W. 

Var. 

10 

55 

00 E. 

Dev. 

12 

23 

45 W. 


Dong. 146° 5’ E. 

4 

Decl. N. deer. 
Sept. 20, i° 10’ 25” 

H. Var. 
58”-3 

6,0)58,4 .20 

Corr. - 1 - 3 .36 

3-7 

9I1 44m 20s 

Corr. decl. 1 .14 .01 N 

4081 

1749 





6,0)21,5.71 



3 - 3 ^ 



Here the longitude in time east to subtract exceeds tbe 
















































34 


SELF-UN STRUCTOR IN NAVIGATION 


time at ship, so we borrow 24 hours and make the date one daj 
less; but we have taken the declination out for the 20th, the 
nearest noon at G reenwich, and worked backwards 3 hours and 
7 tenths, applying the correction for the declination the opposite 
way. The tenths are found by dividing the minutes of the 
Greenwich time by 6. Name true amplitude from W. because 
it is P. M.; towards N. because declination is north. The dif¬ 
ference between the amplitudes is taken for the error because 
they are same name, both north. The error is W. because the 
true amplitude is to the left. The error and variation having 
contrary names, are added to find the deviation, and, when 
error and variation have contrary nam^es, name the deviation 
same as the error. 

EXAMPLES FOR PRACTICE. 

1. 1900, August 17th 5 h 38 m 29 s P. M., apparent 
time at ship; Lat. 22° 56' S.; Long. 23° 35' W.; sun’s com¬ 
pass amplitude W. 20° 30' N.; variation 10° W. Required 
compass error and deviation. 

2. 1900, September 15th 5 h 59 m 30 s A. M., apparent 
time at ship; Lat. 44° 1' S.; Long. 144° 17' E.; sun’s com¬ 
pass amplitude E. 5° 49' S.; variation 10° 5' E. Required 
compass error and deviation. 

3. 1900, October 4th, 6 h 16 m 10 s A. M., apparent time 
at ship; Lat. 24° 59' N.; Long. 160° 5' W.; sun’s compass 
amplitude E. 11° 27'N.; variation 12° E. Required compass 
error and deviation. 

4. 1900, July 23rd, 7 h 27 m 50 s P. M. apparent time 
at ship; Lat. 49° 29'; Long. 177° 59' E.; sun’s compass 
amplitude W. 23° 30' N.; variation 12° E. Required com¬ 
pass error and deviation. 

5. 1900, November 6th 3 7h 33 m 06 s P. M., apparent 
time at ship; Lat 43° 28' S.; Long. 123° 34' E.; sun’s com¬ 
pass amplitude W. by S 4 S.; variation 8° 30' W. Required 
compass error and deviation. 

Answers at the end of the Guide.. 


LONGITUDE BY CHRONOMETER. 


33. Mean Time at Greenwich. Apply the given error to 
the chronometer time; add if slow; subtract if fast. Then 
apply the accumulated rate, add if losing, subtract if gaining; 
and the result is the mean time at Greenwich, expressed, M. 
T. G. The accumulated rate is found by multiplying the 
daily rate by the days and tenths of a day that have elapsed 
since the chronometer error was found, till the time as 
now shown by the chronometer with its original error applied. 
The tenths of a day are found by dividing the hours and tenths 
of an hour of the chronometer time, after the error is ap¬ 
plied to it by 24. (47.) Tenths of an hour are found by 

dividing the minutes by 6. 

Suppose we have 6 h 54 m. The 54 m divided by 6 gives 
9 tenths; thus we have 6.9 h, and 69 divided by 24 gives 3 
nearly, or 3 tenths of a day. 

Sometimes, in the examples, the daily rate is not given, 
but the chronometer errors are stated for two given dates. In 
this case, if both errors are fast, or both slow, we subtract the 
less from the greater; but if one is fast and the other slow, add 
them together. Reduce the result to seconds by multiplying the 
minutes by 60 and adding in the seconds; divide this result by 
the number of days between the two given dates, and we have 
i he chronometer’s daily rate. Now , is it gaining or losing? 

When both errors are fast. 

If the first is less than the second, gaining. 

If the first is greater than the second, losing. 

When both errors are slow— 

If the first is less than the second, losing. 

If the first is greater than the second, gaining. 

W T hen one error is fast and the other slow— 

If the first is fast and the second slow, losing. 

If the first is slow and the second fast, gaining. 

34. Declination for Greenwich Time. Look up the de¬ 
dination for the day on page 2 of the month in the Nautical 


36 


SELF-INSTRUCTOR IN NAVIGATION 


Almanac, and correct it for the hours and minutes by the “vari¬ 
ation in 1 hour (18). 

35. Polar Distance .—Subtract the corrected declination 
from 90° if the declination and latitude are the same name; 
but add 90° to the corrected declination if declination and lati¬ 
tude are different names. The result will be the polar distance. 

Note .—When the latitude is 0°, the declination may either 
be added to or subtracted from 90° for the polar distance. 
When the declination is 0° the polar distance is 90°. 

36. Equation of Time for the Greenwich Time. Take it 
out from page 2 of the month, Nautical Almanac, for the Green¬ 
wich day; and the variation in 1 hour. Multiply this hourly 
variation by the hours and tenth of an hour in the Greenwich 
time; point off from the right all decimals; and the result to 
the left is the correction for the equation of time in seconds; 
add if increasing; subtract if decreasing. Always note the rule 
for applying the equation of time, given at the head of the 
column, and place the sign + or — beside your work. 

37. The True Altitude. To the observed altitude apply 
index error, if any, add if +, subtract if —; dip for height of 
eye from Table 14 Bowditch, or 5 Norie; always subtract; 
sun’s correction (refraction and parallax), Table 18 Norie, or 
corresponding table in Bowditch, always subtract; sun’s semi¬ 
diameter from page 2 of the month, Nautical Almanac, for the 
date of the example, lower limb add, upper limb subtract. Tina 
result is the true altitude. 

Note .—Table 9 Norie gives one correction for a lower limb 
observation which includes dip, refraction, parallax and semi¬ 
diameter. 

38. The Hour Angle. Add together the true altitude, 
latitude and polar distance; divide the sum by 2 for the half 
sum. From the half sum subtract the true altitude, and name 
the result remainder. Take out from Table 44 Bowditch, or 25 
Norie, the logs, secant of the latitude, co-secant of the polar 
distance, co-sine of the half sum and sine of the remainder. 
Add these four logs together, rejecting all tens in the indices, 
and the sum will be the log of the hour angle found in Table 31 



CHRONOMETER 


37 


Norie. When using Bowditch, reject tens in the indices of se¬ 
cant and co-secant; add up the four logs and divide the sum by 
2. The result is the log sine of the hour angle found in Table 
44 Bowditck. 

Note. —When the polar distance is greater than 90°, take 
out the secant of the corfected declination instead of the co¬ 
secant of the polar distance. 

39. Apparent Time at Ship. Right below the hour angle 
place the date as given at the head of the example, the ship date, 
and Oh 0m Os; and if P. M. add; but if A. M. subtract the 
hour angle from the ship date by borrowing 24 hours, and make 
the date one day less. This will be the apparent time at ship. 

40. Mean Time at Ship. To the apparent time at ship 
apply the corrected equation of time as directed in the Nautical 
Almanac. We then have the mean time at ship. 

41. The Longitude. Place the mean time Greenwich 
under the mean time at ship and take their difference. The 
result is the longitude in time, which, converted into longitude, 
is the longitude of the ship. Tables 7 Bowditch, or 19 Norie 
may be used for this purpose; or multiply by 60 and divide by 
4; or we may multiply by 3 and then by 5, which is easier. 

42. Name the Longitude. If mean time Greenwich is 
greater than mean time at ship, name the longitude west. But 
if the Greenwich time is less than the ship time, name the longi¬ 
tude east. 

Greenwich time best, longitude west. 

Greenwich time least, longitude east. 

Notes. —When latitude and corrected declination are both 
nothing, the true altitude subtracted from 90° 0' 0" and re¬ 
duced to time by multiplying by 4 and dividing by 60, will be 
the hour angle. In some examples, the latitude at noon is 
given; it will then be necessary to reduce that latitude to the 
time of sights, by the course and distance run in the interval, 
in order to have the proper latitude to work for the longitude. 
Then you may carry ship’s position on to noon. 


38 


SELF-INSTRUCTOR IN NAVIGATION 


EXAMPLE 1. 

1902, February 8th, A. M. at ship; Lat. 48° 8' N.; ob¬ 
served altitude sun’s lower limb 10° 37' 00"; eye 28 feet; chro¬ 
nometer time, February 8 d 5h 17 m 6 s, which was fast up to 
date lm 31s on mean time Greenwich; index error —30". 
Find the longitude. 


d. h. m. s. 


Chron. Feb. 8 

VO 

u-> 

Alt. 

Decl. S. Deer. 


H’rly Var. 

Err. Fast, — 

I 31 

10® 37’ 00” 

15 ° 

ii* 

17 ” 


47 ”-i 

M, T. G. 8 

5 15 35 

I- E- — 30 

Corr. — 

4 - 

IO 


5 -3 



10. 36. 30 

Corr. Decl. 15. 

7 . 

7 


1413 


Corr. T. 9 Norie 

+ 6. 6 

9O. 

0. 

0 


2355 


True Alt. 

iO. 42. 36 

P. Dist. 105. 

7 - 

7 

6 <°L 

24.9-63 


4' io” 


Alt. io° 42’ 36” Equ. Time Incr. 

Lat. 48 . 8 . 0 . 0.175614 i 4 m 22 s 


P. D.-. 

Sum. 2 ) 

Half Sum- 
Remainder. 


IQ 5 - 7-7 • 0.015294 

163 -57 -43 


Corr. _1 

Corr. E- T. J4_23 


81 .58 .51 . 9 .M 4453 

71 .16 .15 . 9 9/6361 Hour Angle. 

.9.311722= 3I1 35m 22s 

8 d . o .00 .00 


A. T. S. 7 .20 .24 

.38 

Equ. Time .14 

.23 

M. T. S. 7 -20 .39 

.01 

M. T. G.~. 8 .5 .15 

•35 

8 h 36 m 34 s = 
3 

25 -49 

.42 

5 

Long. 129° 08’ 

30” W 


H-To App. Time. 


Table 19 None 
129® 08’ 30” W. 


H. Var. 
s.12 
5-3 

3* 

60 

•635 


Here, no daily rate is given for the chronometer, but the 
error is given up to date. One correction has been used for the 
altitude from Table 9 Norie. The secant of the corrected dec¬ 
lination has been taken out because the polar distance is more 
than 90°. The logs are taken out for nearest one-half minute of 
arc only. Table 31 Norie has been used for the hour angle. 


EXAMPLE 2. 

1902, March 9th, P. M. at ship. Lat. 44° 43' S.; ob¬ 
served altitude sun’s lower limb 32° 10' 40"; height of eye 18 
feet; time by chronometer March 9 d 5 h 58m 28 s, which was 
fasi on mean noon at Greenwich on January 21st 8 m 12 s, and 
gaining daily 2s; index error -1' 25 ". Required the longi¬ 
tude. 
































CHRONOMETER 


39 


£hron. Mar_ 

Err. Fast. 

9 d 

5 h 

58 m 

8 

28 s 
.12 

Acc. Rate Gain 

9 

5 

.50 

. 1 

.16 

•34 

M. T. G. 

9 

5 

.48 

.42 


Days in Jan. io 


Feb. 

Mar 


Acc. Rate... 

Decl. Mar. 9 
Corr. 

Corr. Decl. 

< 

Polar Dist. J 


28 

_9 

47 


47-2 

2 


For Tenths of a Day. 

5 h 50m = 5 h .8 

2 4)_58 

— 2 Tenths of a Day 


60) 94-4 
1 m 34s 

4° 44’ 4i’ 
~ 5 -39 

4 -39 -02 
o .00 .00 
5 .20 .58 


S. deer. 


Var. in 1 hour. 
58” .5 
5 -8 

4680 

_2925__ 

33(9-3° 
Corr. 5’ .39” 


Equ. of Time Deer. 

10m .53s .0 
Corr. — 3-6 

io 49_^4 

-f- to app. time 


Corr. 


H. Var. 

Obs. Alt. 

32° 

io’ 

40" 

os.62 

I. E. 

— 

.1 

.25 

5 -8 


32 

•9 

.15 

496 

Dip 18 ft. 

— 

4 

•9 

310 


32 

•5 

.6 

3S.596 

Corr. Tab. .18 

— 

1 

.24 



32 

•3 

.42 


Semidia. 

-f 

16 

•7 


True Alt. 

32 0 

19’ 

49 


Alt. 

Eat. 

P. D. _ 

2 I_ 

H. Sum 
Rem. 


3 2 ' 

44 

_&5_ 

162 

81 

48 


19’ 

•43 

.20 

•23 

.11 
• 52 


49” 

.00 

47 

• 53 
.04 


148378 

001432 

95 
184651 
876899 
7 


Hour Angle 
h. m. s. 


9 . 211462 = 

3 

9d 0 

10 19 
0 0 

A. T. S. 

9 3 

10 19 

Equ. Time 

+ 

10 .49 

M. T. S. 

9 -3 

.21 .8 

M. T. G. 

9 .5 

h. 

.48 .42 

m. s. 

Longitude 36® 53’ 30” West 

— 2 

27 34 


The above is worked out to seconds of arc for example only, 
but the nearest half-minute is considered sufficiently accurate. 

EXAMPLE 3 . 

1902 . March 31 st, A. M. at ship; Lat. 11 ° 2' S.; ob- 
















































40 


SELF-INSTRUCTOR IN NAVIGATION 


served altitude sun’s lower limb 33° 59' 10" ; eye 26 feet; time 
by chronometer 30d 16 h 10m 10 s, which was fast on mean 
time Greenwich 11 m 27 s on March 1st, and gaining daily 
4.7 s; index error +2' 53". Required the longitude. 


d. h. m. s. Decl. N.Incr. H. Var. 


Chron. Mar. 30 16 10 10 Mar. 31st 3 0 54’ 7”— 58” .2 

Err. fast — 

11 .27 Corr. 

-7-51 8 .1 

30 15.58.43 Corr. de d. 3 .46 .16 N. 582 

Accd. rate, gain — 

2 .21 

90 OO OO 4656 

M. T. G. 3od 

15.56.22 P. D. 

93 .46 .16 6 4 o) 47,1 .42 


24 

7 ’ 5 1 ” 

Time from Noon 3rd 

8.03.38 


Equ. Time deer. 

H. Var. 


4 m 28 s 

s .76 

Obsd. Alt. 33 0 59’ io” 

Corr. -f- 6 

8 . 1 

I.E. + 2 53 

Corr. E. T. 4m 34s 

76 

34 .02 .03 

— 

608 

Corr. Tab. 9 Norie + . 9 .42 

+ to app time 

6s .156 

True Alt 34 .11 -45 



Daily gain 4s .7 

Days elapsed 30 



6,0) 14,1 .0 



Accd. rate 2m 21s 

Ait.. 



Lat. 


. 0 . 008103 Sec. 

P. D 


. 0 . 000939 Sec. of corr. decl. 


2 ) 139 .00 .01 



69 .30 .00 

. 9 . 544325 Cosine 


35 .18 .15 

. 9 . 761821 Sine 

Hour Angle. 

3h 36m 18s 

. 9 • 315188 


3id .0 .0 .0 


A. T. S. 



Equ. Time... 



M. T. S. 

.. 3od .20 .28 .16 


M. T. G. 

.. 3od .15 .56 .22 


Long, in Time. 4h 3101548= 



,l U° Pg .67°5S’3o”B. 


In this example the declination and equation of time are 
taken out for March 31st, the nearest noon, and worked back¬ 
wards 8.1 hours to the Greenwich time. 

The secant of the corrected declination is used, because the 
polar distance exceeds 90°. The logs are taken out to nearest 
one-half minute of arc from 25 Norie, useful for that purpose. 

EXAMPLE 4. 

1902, October 4th, A. M. at ship; observed altitude sun’s 













































CHRONOMETER 


41 


upper limb 53° 45' 30" ; height of eye 26 feet; time by chro¬ 
nometer October 4 d 6 h 49 m 07 s, which was slow on mean 
noon at Greenwich 12 m 48 s on June 30th; and slow on mean 
noon at Greenwich 9 m 30 s on August 24th; index error 4-1' 
16"; latitude at noon 17° 21' N:; run between sights and noon 
S. E. true 17 miles. Required the longitude at noon. 


Green. Time. 

Oct... .4th 6h 49m 07s 
+ 9 30 

4 6 58 37 

— 2 29 


M.T.G.4th 6h 56m 08s 


Decl. S. Incr. 
Oct.. 4th 4 0 05’ 09” 
+ 6 .40 

4 .11 .49 S. 
90 .00 .00 
P. D. 94 .11 .49 


H, Var. 
58” 
6.9 


522 

348 

6 t o) 4o ( o.2 
6’ 40” 


Equ. H. 
Time Incr. Var. 
11m 01s — os.77 
+ 5 6 .9 

nm 06s 693 

Ap.Time. 5 - 3 J 3 


Minor Corrections. 
12m 48s slow. 

9 .30 slow. 

3 .18 
60 

55 ) 198 (3 s.6 daily gain. 
330 


July 31 days. 
Aug. 24 “ 

55 days. 

Aug. 7 days. 
Sept. 30 “ 

Oct. _4 “ 

41 days. 


24 ) 6.9 hours. 

.3 of a day. 


41.3 days. 

Rate. 3.6 seconds. 

2478 

_I23?_ 

6,0 ) 14,8.68 
Accd. Rate 2m 29s 


Obs. Alt. Sun’s Upp. Limb. 

53 ° 45 ’ 30 ” 

I. E. 4 - r .16 


Dip. 26 Ft. 

53 46 46 
— 5 -oo 

Sun’s Corr. 

53 4 i 46 
— 0 .36 

Sem. dia. U. L.. 

53 4 i .10 
— 16 .01 

True Alt. 

...53° 25’ 09” 


H. Angle .... 

A. M. 

A. T. S. 

Equ. Time... 

M. T. S. 

M. T. G. 

Long, in Time 


Run S. E. True, 17 Miles = 

Lat. Noon.17 0 21’ N. 

Diff. Lat. .12 N. 

Lat. Sights.17 .33 N. 


Alt. 53 ° 2 5 ’ 

Lat. 17 .33 . o . 020700 

P. D. 94 .12 . o . 001168 

2 ) 165 .10 

82 .35 . 9 . 110873 

_ 29 .10 . 9 . 687843 

. ih 59m 14s . 8 . 820584 

. 4d o o o 

. 3d 22h 00m 46s 

. — 11 .6 

. 3d 21 .49 .40 

. 4 6 56 .08 

9 . 6 .283 

_ 3 

27 .19 .24 

__ 5 

136 .37 .00 West. 

— 13 .00 E. 

136° 24’ 00” West. 


Long at Sights 
Dep. 12’ = Diff. Long. = 
Long, at Noon. 


The run S. E. is reversed mentally when allowing the diff¬ 
erence latitude to find the latitude at sights. The hour angle 
















































































42 


SELF-INSTRUCTOR IN NAVIGATION 


is subtracted from noon of the 4th because it is an A. M. sight. 


EXAMPLES FOR PRACTICE. 


1. 1902, December 17th P. M. at ship; in Manila Bay, 
in Lat. 14° 34' 30" N.; observed altitude sun’s lower limb 27° 
04' 10"; height of eye 28 feet; time by chronometer 16 d 19 h 
18 m 39 s, which was fast up to date 1 m 54 s; index error -0' 
20". Required the longitude for a check on the chronometer. 

2. 1902, June 4th A. M. at ship; latitude 52° 10' 30" 
N.; observed altitude sun’s lower limb 41° 05' 30"; eye 28 
feet; time by chronometer 4 days, 7 h 2 m 9 s, which was slow 
37 m 12 s on May 1st, and losing 1.7 s daily; index error -2' 
41". Required the longitude. 

3. 1902, December 10th, P. M. at ship; Lat. 29° 40' 30" 
N.; observed altitude sun’s lower limb 12° 32'; eye 26 feet; 
time by chronometer 9 days, 19 h 4 m 4 s, which was 2 m 1 s fast 
up to date; index error + 30". Required the longitude at sights 
and at noon. Run from noon till sights 35 miles S. 40° W. 


true. 


4. 1902, May 11th, A. M. at ship; Lat. 39° 59' S.; ob¬ 

served altitude sun’s upper limb 11° 2' 6"; eye 24 feet; time 
by chronometer, May 11 d 7 h 3 m 41 s, which was fast 2m 4s 
on mean time Greenwich on February 2nd, and was slow 1 m 
17 s on mean time Greenwich on March 29th; index error - 3' 
05". Required the longitude. 

Answers at the end of the Guide. 


TIME PROBLEMS. 


43.—To Convert Longitude Into Time. —Multiply the 
longitude by 4 and divide by 60. The result will be its time 
equivalent. 


EXAMPLE 1. 

Turn 21 0 44' 31" into time. 
4 


Convert 175 0 13' 47" into time 
4 


EXAMPLE 2. 


6,0 ) 8 < 6.58.Q4 
Ans. 1 h 26m 58s.07 


6,o ) 7 Q<o-55-o 8 
Ans. nh4om55S. 13 











TIME PROBLEMS 


43 


44-—To Convert Time Into Longitude.— Multply the 
time by 60 and divide by 4. The result is its longitude value. 
example 3. 

Turn 6h 14m 12s into arc. Or thus 6h 14m 12s 

60 120 5 

4 ) 374 132 31. 11.00 

93 ° 33 ' qq/ _ 3 _ 

93 ° 33 ' 00* 

The second method in the above example seems easier, and is 
equal to multiplying by 15, which is the same as multiplying by 
60 and dividing by 4, as shown in the first method. 

Note.—Tables 7 Bowditch and 19 Norie; also tables A and B 
Norie, are useful in facilitating the above problems. 

45. —To Convert Minutes and Seconds Into the Deci¬ 

mal of an Hour.— 

First reduce the seconds to the decimal part of a minute by 
dividing them by 60, then divide the minutes and decimal of a 
minute by 60. The result is the decimal part of an hour. 
EXAMPLE 4 

Reduce 3I1 40m 36s to hours and decimal part of hour. Thus: 
6036 Seconds. 

60:40,6 Minutes and decimal part of minute. 

| 3.68 Hours and decimal of hour nearly. 

46. —To Convert the Decimal of an Hour Into Min¬ 

utes and Seconds. 

Multiply the decimal part in succession by 60, as follows: 
example 5 

Reduce 3b.68 to hours, minutes, and seconds. 

3h.68 

60 

40.80 Minutes Therefore, 3.68 hours—3 hours, 

60 

48.00 Seconds 40 minutes, 48 seconds, nearly. 

Note.—It is usual for all practical purposes, simply to divide 
the minutes by 6 to obtain the decimal of an hour. If the seconds 
reach 30 or more, make the minutes one more. 

2 example 4 

Reduce 3I1 40m 36s to hours and loths of an hour. Thus: 

6I41 

‘3.7=3 hours and 7 tenths nearly. 













44 


SELF-INSTRUCTOR IN NAVIGATION 


Here the seconds exceed 30, so we increase the minutes by one. 
47.—To Reduce Hours to the Decimal of a Day.— 
Amnex a cipher to the hours and divide by 24. 

2 example 5 

Reduce iod 4I1 56m to days and decimal of a day. Thus: 

24) 50 (21 Therefore, iod 4I1 5601=10.21 days. 

48 

20 Note.—4h 56m are roughly taken as 5 hours. 

Note.—The decimal part of a day is required approximately 
only, when figuring out the accumulated rate of a chronometer. 
One place of figures is considered sufficiently near; so that 10.2 
days is the approx, answers to the last example. 


COMPASS ERROR BY AZIMUTH. 

The time given in the example may be mean time at ship, 
or apparent time at ship; but whatever time is given, we must 
reduce it to mean time at Greenwich, so as to correct the dec¬ 
lination and equation of time for the Greenwich date. Mean 
time at Greenwich is sometimes given. 

Mean Time at Ship Given. —If P. M., write the time 
down as given, with the date at the head of the question. But 
if A. M., add 12 to the hours and make the date one day less. 

For the Mean Time at Greenwich. Under the mean time 
at ship as now written place the longitude in time, and add if 
west, subtract if east. The result is mean time at Greenwich. 
The longitude is turned into time by multiplying by 4 and 
dividing by 60 ( 43 ), or by use of Tables 7 Bowditch or 19 
Norie. 

Note. —If longitude west added exceeds 24 hours, subtract 
24 hours and call the date one day more. If longitude east to 
he subtracted is greater than the hours, minutes and seconds of 
the mean time at ship, borrow 24 hours and call the date one 
day less. 

Declination for the Greenwich Date. Take out the dec¬ 
lination for the Greenwich date from page 2 , Nautical Al¬ 
manac, and its variation in 1 hour; multiply the variation in 




AZIMUTH 


45 


1 hour by the hours and tenths of an hour of the Greenwich 
time, and score off the decimals from the right. What remains 
will be the correction for the declination; add, if increasing; 
subtract, if decreasing. 

Polar Distance. When latitude and corrected declination 
are the same name, subtract the corrected declination from 90 ° 
0 ' 0 "; but if different names, add 90 ° to the corrected declina¬ 
tion. The result in either case is the polar distance. 

Note. If the Latitude Is Nothing. When wanting to 
find the polar distance or name the true azimuth, v suppose the 
latitude to have the opposite name to that of the corrected dec¬ 
lination. 

Equation of Time for Mean Time Greenwich. Take out 
the equation of time for the Greenwich day from page 2, Nauti¬ 
cal Almanac, and its variation in 1 hour, multiply the variation 
in 1 hour by the hours and tenths of an hour; score off all 
decimals from the right of the product. What is left is the 
correction (in seconds) for the equation of time; to be added 
if the equation of time is increasing, and subtracted if decreas¬ 
ing. 

The True Altitude is found by applying to the observed 
altitude index error +, add; -, subtract: dip, for height of 
eye, always subtract; sun’s correction, subtract, and sun’s 
semi-diameter from Nautical Almanac for the date, add for a 
lower limb; subtract for an upper limb. The altitude is cor¬ 
rected same as.in meridian altitude ( 19 ) and chronometer 
questions ( 37 ). Table 9 Norie may be used for a lower limb 
only ; it gives one correction. 

Now Find the True Azimuth. Add together the polar 
distance, latitude and true altitude; divide the sum by 2; and 
take the difference between the half sum and the polar distance 
for the remainder. Then take out from Tables 44 Bowditch, 
or 25 Norie, secant of the latitude, secant of the altitude, co¬ 
sine of half sum, and co-sine of remainder. Subtract tens from 
index of secants; add these four logs; divide the sum by 2. 
Find this log as near as you can in the sine column of the same 
table, and the degrees and minutes corresponding will be half 


46 


SELF-INSTRUCTOR IN NAVIGATION 


the true azimuth, which multiplied by 2 will give the true 
azimuth. 

48. To Name the True Azimuth. Reckon from south 
in north latitude and from north in south latitude; towards 
east if A. M., towards west if P. M. 

Note —If the latitude is nothing, name the true azimuth 
from the opposite pole from which the polar distance has been 
reckoned. 

49. Find the Compass Error. If the compass azimuth 
given in the example is the same north or south, as the true 
azimuth, place the compass azimuth below the true. But if one 
is north and the other south, then first subtract the true azi¬ 
muth from 180°, and name the remainder true azimuth north 
or south, same as the compass azimuth, and place the compass 
azimuth under it. Now, if the true and the compass azimuths 
are both east or both west, subtract the less from the greater, 
but if one is east and the other west, add them together. The 
result is the compass error. 

Name the Error. Looking from the center of the com¬ 
pass towards the margin; if the true azimuth is to the right of 
the compass azimuth, the error is east; but if the true azimuth 
is to the left of the compass azimuth, the error is west. 

Find the Deviation. Bring down the variation given in 
the example, under the error. If one is east and the other west, 
add them together; but if they are the same name, subtract the 
less from the greater. The result is the deviation. 

To Name the Deviation. When the error and variation 
have the same name, mark the deviation the same as the error 
if the error is greatest ; but contrary to the error if the error 
is less than the variation. When the error and variation have 
contrary names, mark the deviation same as the error. Or, 
using the compass card, mark ofi the error and variation at the 
north point of the compass, to the right of north if east, but to 
the left of north if west. Now, if the error is to the right of the 
variation, the deviation is east, but if the error is to the left of 
the variation, the deviation is west. 

Note. —If the variation is 0®, the deviation is the same 


AZIMUTH 


47 


as the error, and the same name. When the error is 0°, the 
deviation is the same as the variation, but of a different name. 
When latitude and declination are both nothing, the true azi¬ 
muth is 90°, east if A. M.; west if P. M. If the compass azi¬ 
muth is given due east, call it 1ST. 90° E., or S. 90° E.; and if 
given due west, call it N. 90° W., or S. 90° W., reckoning from 
north, or south, like the true azimuth. 

Greenwich Time Given. If any error on mean time is 
given, add if slow; subtract if fast. 


EXAMPLE 1. 

1902, January 10th, P. M. at ship, at4h29m28s mean 
time at ship; Lat. 32° 47' S.; Long. 28° 4' W.; sun’s bear¬ 
ing by compass W.xX.^X.; observed altitude sun’s lower limb 
34° 12' 17"; height of eye 22 feet; variation 5° 29' W. Re¬ 
quired sun’s true azimuth, error of compass and deviation. 

Long 


M. T. S. iod 4h 29m 28s 

Long, in Time... . -f- i .52 .16 
M. T. Green. iod .6h .2im.44* 


4’ W 
4 


6, 0) 11,2 .16 
ih.52111 .16s 


Decl. S. Deer. 
22° 3’ 14” 

— 2 .20 
22 .0.54s 
90 .0 .0 


Polar Dist... 67 .59 .06 


Hourly Var. 

2 l ”.8 

_ 6.4 

_ $ 

6.0) i&9 -5 2 

2 ’ 20 * 


Error 


Obsd. Alt. L.L.. 34°:2’i7” 

Dip. — 4.36 

34 .7 .41 P. D.. 67°59’ 6” 

Sun’s Corr. — .1 .17 Lat... 32 .47 .0 Sec.0.075346 

34 .6 .24 Alt... 34 .22 .41 Sec..0.083357 

Sem. dia. -{-.16.17 2) 135.8.47 

True Alt. 34 0 22’ 41” 67.34.23 Cosine .9.581465 

- : 0.24.43 Cosine .9.999989 

2 )19.74015 7 

Half T. Azim.47 0 51Sine... .9.870078 

2 

True Azim. N. 95 .43 W 

Comp. Azim. N. 73 .7V 2. W 

Error. 22 .35% w 

Var. 5 .29 W 

Deviation. 17® .6’&W 



EXAMPLE 2. 


1902, April 3rd, A. M. at ship, 8h 59 m 47 s mean time 
ship; Lat. 31° 59' S.; Long 67° 50' E.; sun’s compass azi¬ 
muth E. | S.; observed altitude sun’s lower limb 35° 1' 3"; 
eye 24 feet. * Required the true azimuth and error of the com¬ 
pass; and supposing the variation 15° 45' W., find the devia¬ 
tion. 












































48 


SELF-INSTRUCTOR IN NAVIGATION 


M. T. S. ad 2oh 59m 47s 

;Tong. in Time... — 4 .31 .20 

1 M. T. G. 2d 16 .28 Tl 

-- 


,Obs. Alt. 35 0 1’ 3” 

‘Corr. Tab. 9 Norie... -/- 9 54 

True Alt.j 35 °_ 10 ’ 57 ” 


Tong.. 67° 50’ E Decl. N. Incr. H. Var. 

_4 4° 4 o’ 28” 5 7”.8 

6,o) 27,1. 20 15 -54 16 .5 

4h 31m 20s Decl... 4.56.22 N 2890 

- • 90 .0 .0 3468 

P. D 94 ° 56 ’ 22" 578 


6 ,0) 95,3-7 0 

15’ 54’ 


P. D 
Tat.. 
Alt... 


Half T. Azim. 27 0 49’ J 4 

2 


T. Azim. 

N 

55 

•39 

E 



180 

.0 


True Azim. 

.. S 

124 

.21 

E 

Comp. Azim... 

. S 

87 

.11 

E 

Error,. 


37 0 

10 

w 

Var. 


15 

•45 

w 

Deviation.. 


21 ° 

•25’ 

w 


... 94° 56’J4 

... 31 .59 Sec.0.071501 

.. . 35 .11 Sec.0.087612 

2 ) 162 .6^4 

81 .3 Cosine .9.101933 

13 - 53 l A Cosin e .9 987108 

2 ) 19 338154 

= Sine = 9.669077 


EXAMPLE 3. 


Error 




1902, October 4th, A. M., 9 h 32 m 20 s mean time ship; 
Lat. 33° 36' X.; Long. 133° 36' W.; sun’s compass azimuth 
E. x S.; observed altitude sun’s upper limb 40° 20 v 30"; eye 
26 feet; index error +2' 34"; variation 14° E. Required the 
true azimuth, compass error and deviation. 


M. T. S.3d 2ih 32m 20s Long. 133° 36’ W. Decl. S. incr. H. Var. 

Long, in Time .-H- 8 54 24 4 4 ° 5 ’ 9 ” 58” 

M. T. G.4 d 6h 26m 44s 6,0 )53,4 24 6 11 6 -4 

8h 54m 24s 4 11 20 S 232 

===== 90 o o 348 

**. P.D... 94° ii , 2 o ” 6,0 )37,1.2 

“ 6’ ii ” 


£rr»r 


Obs. Alt. 40 0 20’30’ 

I. E. . -II- 2-34 

40 .23 .4 

Dip. — 5 -° 

4 o .18 .4 

Sun’s corr. — i .o 

40 .17 .4 

Sem.dia. U.T. — 16 .1 

True Alt. 40° i’ 3” 



2 

T. Azim. .. S 47 .46 E 

C. Azim.... S 78 .45 E 

Error. 30° 59’ E 

Var . 14 ,o E 

Deviation. i6 w 59’ E 





























































































AZIMUTH 


49 


EXAMPLE 4. 


1902, September 23rd, P. M. at ship; Lat. 34° 23' X.; 
Long. 23° 24' E.; sun’s compass azimuth west; observed alti¬ 
tude sun’s lower limb 31° 49' 10"; eye 22 feet; time by 
chronometer, correct for mean time Greenwich, September 
23 d, 1 h 41 m 21s. Required the true azimuth and error of 
compass; and the variation being 10° W., find the deviation. 


d h m 

M. T. G.Sept. 23 1 41 

s Decl. N. Deer H. Var. 

21 o« n’ 44” 58” .4 

1 39 1 -7 

P. D. Sgf'sd’ 

Decl. o° io’ 5” 

4088 

E&t. 34 .23 .0.08340 

90 0 0 

584 

Alt. 31-59 -0.07150 

P.D. 89° 49’ 55” 

6,0)9,9.28 

2)156 .12 


i’ 39 ” 

78 .6 .9 .31430 
11.44.9,99083 



2) 19 .46003 



9 .73001: 

=% True Azim. 

3 *° 29 ’ 


True Azim. S 64 .58 W 

Comp. Azim ...S 90 .00 W 

Error. 25 .02 W 

Var. 10 .00 W 

Deviation. 15 0 02’ W 


Obs. Alt. 31 0 49* 

Corr. Tab. 9 Norie 9 


10” 

.48 


-/■ 


True Alt. 3 i» 58' 58” 



Dtviatiem 




4 


In the preceding examples the logs have been taken out, 
in some cases to the nearest half-minute, and in others to the 
nearest minute of arc only. The nearest minute may be con¬ 
sidered sufficiently accurate in working an azimuth. 

The following examples for practice have been worked 
to the nearest half-minute of arc, and the declinations corrected 
from the nearest noon. The altitudes are corrected by one 
correction from Table 9 Norie , except in the case of an upper 
limb observation, when dip, sun’s correction and semi-diameter 
are applied separately. The student may use the tables he likes 
best, or is accustomed to. The result will be about the same. 

EXAMPLES EOR PRACTICE. 

1 . 1902, March 15th, P. M. at ship, 2 h 19 m 00 s mean 

time ship; Lat. 33° 30' S.; Long. 79° 10' E.; sun’s compass 
azimuth X. W. ^ X.; altitude sun’s lower limb 46° 2' 45"; 


































50 


SELF-INSTRUCTOR IN NAVIGATION 


eye 22 feet; variation 16° W. Required the true azimuth, 
compass error and deviation. 

2 . 1902, April 5th, A. M. 9 h 48 m 15 s mean time ship; 
Lat. 32° 32' S.; Long. 82° 32' W.; altitude sun’s upper limb 
40° 23' 14" ; eye 26 feet; compass azimuth N. E. x N.; varia¬ 
tion 17° 11' E. Find true azimuth, error of compass and 
deviation. 

3. 1902, May 6th, P. M. 3 h 47 m 10 s mean time ship; 
Lat. 34 ° 5' N.; Long. 122° 59' W.; altitude sun’s lower 
limb 37° 32' 2" ; eye 25 feet; compass bearing W. 3° 20' N.; 
variation 14° 5' E. Find true azimuth, compass error and de¬ 
viation. 

4. 1902, June 5th, A. M., 9 h 00 m 20 s mean time ship; 
Lat. 33° 1' N.; Long. 137° 3' E.; altitude sun’s lower limb 
50° 02' 14"; compass azimuth E. -J N.; eye 24 feet; variation 
2 ° 4' W. Required true azimuth, compass error and deviation. 

Answers at the end of the Guide. 


TIME AZIMUTH. 

The Sun's True Bearing for every ten minutes between 
sunrise and sunset, is given in the azimuth tables, issued by U. 

S. Navy Department; also, for every 4 minutes, in Burdwood’s 
and Davie’s Azimuth Tables. In the following examples the 
American publication has been used. 

These tables are to be entered with the latitude, the appar¬ 
ent time at ship, and the corrected declination. The latitude is 
found at the top of the page, and the apparent time at ship at the 
sides, A. M. on the left, P. M. on the right. The declination Is 
also found at the top, under the latitude. Be careful when 
looking up the latitude to take it out according as the declina¬ 
tion and latitude have the same, or different names, as the case 
may be. 

Apparent time at ship must always be used to get the 
sun’s true bearing from these tables. If mean time at ship ‘s 
given in the example, it must be reduced to apparent time at 
ship by applying the equation of time, corrected by its variation 


TIME AZIMUTH 


51 


m 1 hour for the hours and tenths of an hour of the Greenwich 
date. The rule at the head of the equation of time column will 
guide you in applying it to mean time. The result will be 
apparent time ship. 

If Greenwich mean time is given apply the longitude in 
time; east, add; west, subtract. The result is mean time ship, 
then apply the equation of time as above directed, and we have 
apparent time ship for the tables. When the time is given 
Greenwich mean time and the example begins with A. M. at 
ship, then this apparent time at ship will exceed 12 hours, and 
we must subtract 12 hours before entering the tables. 

The declination should be taken out and corrected for the 
Greenwich time. Or, if taken out for ship’s date, it should be 
corrected for longitude by Table 21 Xorie. 

Often at the examinations it is considered sufficiently 
accurate to enter the azimuth tables with the nearest degree of 
latitude and declination, and the nearest minute of time; 
though finer results can be reached, if the candidate is fond of 
unnecessary figures. 

Owing to continual change of longitude at sea, the clock 
or watch is usually away off for apparent time at ship; then 
compare the timepiece with the chronometer, noting the time 
by both, say to the nearest half-minute. Allow the error on 
the chronometer to date, work up the longitude by D. R., turn it 
into time and apply to Greenwich time: east, add; west, 
subtract. This is now mean time ship. Apply the equation of 
time, and we have apparent time ship. The difference between 
this and the time noted by the clock or watch is its error. It 
should be corrected for convenience. 

EXAMPLE 1. 

Find the true azimuth for latitude 48° X., at 5 h 40 m P. 
M. apparent time ship; declination 16° X. Answer X. 82° 
43’ W. 

EXAMPLE 2. 

1902, May 25th, Lat. 47° X.; Long. 59° W., at 3 h 50 m 
P. M. apparent time ship; sun’s compass bearing X. 56° 15' 


52 SELF-INSTRUCTOR IN NAVIGATION 


W.; variation 31° W. 

Required the deviation by azimuth 

tables. 


True Azim. 

.N 98° 50’ W 

Comp. Azim 

.N 56° 15’ W 

Error. 

. 42 35 W 

Var. 

. 31 .00 w 

Deviation... 

. 11° 35’ w 

Note the rules at the foot of the azimuth tables for nam¬ 

ing the true azimuth. These tables are self-explanatory. 


EXAMPLE 3. 

1902, February 2nd, Lat. 40° N.; Long. 48° W., 9h 
SO m A. M., apparent time ship; sun’s compass bearing N. 
139° 20' E.; variation 7° 19' W. Find the deviation. 


Per. Azim. Tables, Sun’s True Bearing.N 145 0 19’ E 

Comp. Bearing. N 139 20 E 

Error. 5 59 E 

Var. 7 19 W 

Deviation. 13 0 18’ E 


The azimuth tables may also be used to obtain the true 
bearing of the moon, stars or planets, provided the object’s 
declination is within the limits of the tables. In such cases, the 
hour angle is used instead of the apparent time ship. 

Rule for the Hour Angle. To the astronomical apparent 
time (that is, reckoning from the previous noon) add the ap¬ 
parent sun’s right ascension. The sum is the right ascension of 
the meridian. Now, subtract the body’s right ascension, and 
we have the hour angle needed, to be sought for in the P. M. 
column of the azimuth tables. 



EXAMPLE 4. 

902, May 27th, Lat. 51° N., 11 h 42 m P. M., apparent 
hip; star Spica bear'by compass N. 93° W.; local varia- 
35|° W. Required the deviation. 


A. T. S. 

. nh 

42 m 

Sun’s App. R. A_ 

. 4 

•13 

R. A. of Mer. 

• 15 

55 

Star’s R. A. 

• 13 

20 

Star’s Hour Angle. . 

2 

35 


Enter the azimuth tables with Lat 51° N. stars declina- 

























REDUCTION TO MERIDIAN 


53 


tion 10° 39' S. (latitude and declination contrary names), and 
tlie hour angle 2 h 35 m, and take out from the P. M. column. 


Star’s True Bearing. N 139 0 o’ W 

Star’s Comp. Bearing. N 93 o W 

Error. 46 o W 

Var. ..35 30 W 

Deviation. io° 30’ W 


EXAMPLES FOR PRACTICE. 

1. Find time azimuth for Lat. 34° S., sun’s declination 
14° S.; apparent time at ship 3 h 10 m P. M. 

2 . What is the sun’s true azimuth for Lat. 20° N., decli¬ 
nation 43° S., and apparent time at ship 7h 20 m A. M. 

3. Required sun’s true azimuth for Lat. 33° N., declina¬ 
tion 12° S., and apparent time at ship 9 h 30 m A. M. 

4 Find sun’s true azimuth for Lat. 40° S., declination 10° 
N., and apparent time at ship 2 h 40 m P. M. 

Answers at the end of the Guide. 


LATITUDE BY REDUCTION TO THE 
MERIDIAN. 

The exact time from noon, the latitude by account 
and the corrected declination are necessary in obtaining the 
latitude by this process. To the time by watch as given apply 
its error; -f if slow; - if fast. Then apply the difference of 
longitude in time for the run of the ship since the error on 
apparent time was found; add if easting, subtract if westing. 
The result is apparent time at ship. Now, if it is a P. M. 
example, the apparent time at ship will be 0 hours, some min¬ 
utes and seconds, and these minutes and seconds will be the 
time from noon. But if the example is A. M., the apparent 
time at ship will be 23 hours, some minutes and seconds, reck¬ 
oning from the preceding noon, and this subtracted from 24 
hours 'will be the time from noon. 

We need the Greenwich time for which to take out and 
correct the sun’s declination. To the apparent time at ship 
apply the longitude in time: + if west, - if east. The result is 











54 


SELF-INSTRUCTOR IN NAVIGATION 


apparent time Greenwich. Take out the declination for the 
Greenwich date and correct it in the usual manner for the hours 
and minutes of the Greenwich time. Correct the observed, alti¬ 
tude, also in the usual way. Then take out from tables. 


Time from Noon. Log. rising 29 Norie 

Latitude. Cosine 44 Bowditch, 25 Norie 

Declination. Cosine 44 “ 25 Norie 


Add these logs, rejecting 20 from the index, and take out 
the number corresponding to their sum from 42 Bowditch, or 
24 Norie. To this add the natural sine of the true altitude, 
Table 26 Norie, using five figures only. Seek the sum in the 
same table. The degrees at the foot and minutes at the right 
hand side, natural co-sine, will be meridian zenith distance, 
to be named contrary to the sun’s bearing. 

Now Find the Latitude. Bring down the corrected de¬ 
clination, and if it and the zenith distance have like names, 
add them together; but if contrary names, subtract the less 
from the greater, and the result is the latitude, of the same 
name as the greater. 

Mean Time at Greenwich Given. Take out the declina¬ 
tion and equation of time from page 2, Nautical Almanac, and 
correct them for the Greenwich time as stated, by the variation 
in 1 hour. If chronometer time is given with an error on mean 
time, see that its error is applied, in order to correct the decli¬ 
nation and equation of time for the correct mean time Green¬ 
wich. To this mean time Greenwich we must apply the longi¬ 
tude in time, east +, w r est and call the result mean time ship. 
To the mean time ship apply corrected equation of time by the 
rule at the head of the column in Nautical Almanac. We now 
have the apparent time ship, and this apparent time ship gives 
the time from noon, as prevoiously explained. Remember that 
the latitude by reduction to meridian is the latitude of ship at 
time of observation, so that to reduce the latitude to noon, we 
must allow the difference latitude on the course and distance 
made in the interval. 

Ex-meridian tables are used in practice at sea, from which 
a correction for the observed altitude is taken out by inspection; 
and from the altitude thus corrected the latitude at time of 
observation is found in the same manner as by meridian alti' 





REDUCTION TO MERIDIAN 


55 


tilde j but at the examinations the work is done by calculation, 
as shown in this chapter, or by a similar method. 

EXAMPLE 1. 

1902, January 7th, P. M. at ship; Lat. by account 
27° 3' N.; Long. 67° 15’' W.; observed altitude sun’s lower 
limb south of observer 39° 57' 00"; eye 23 feet; time by watch 
i days, 0 h 22 m 44 s, which was slow 6 m 52 s on apparent time 
ship; difference longitude made, east 21 miles, since error on 
apparent time ship was found; index error - 2' 45". Required 
the latitude by reduction to meridian. 

Decl. S. deer. 


d h m s 
Time by Watch. .7 o 22 44 
Err. slow_+ 6 52 


Diff. long. 

21* E 22 0 27’ 23” 

_4 Corr. — 1 32 


7 o 29 36 6 < o)8 < 4 Corr. decl. 22 0 25 51 
Diff. long. E_ -f- 1 24 1 m 24s -- 

A. T. S.7 o 31 o Long. 67° 15’ W 

Long, in T. W.. -4-4 29 o 4 

A. T. G-7d 5h om os 6 ( o) 26,9 .0 

4h 29m 


H. Var. 
18” .5 

_5 

6<o)9<2-5 
i’ 32” 


Obs. Alt.39*57’ o" 

*. ~ 2 45 

39 54 15 
Dip.— 4 42 


Time from Noon... 31m os Log. ris. 2.96067 

Latitude. 27® 3’ Cosine 9.94969 

Corr. decl. 22° 26* Cosine 9.96582 


Number. 751.9 Log. 

T. Alt. 4o°5’, nat. sine. 64390.1 


_ ,. 39 48 31 

Sem. dia.... -|- 16 17 
True Alt....40 448 


.2.87618 

Nat. cosine. 6si42.o=Mer. Z. dist. 49° 21’ 05” N. 

Decl. 22 25 01 S. 


Latitude. 26° 55’ 14” North 


EXAMPLE 2. 


1902, April 11th, A. M. at ship; Lat account 23° 
40' S.; Long. 118° 20' E.; altitude sun’s lower limb 56° 51' 
57" N. of observer; eye 22 feet; time by watch 10 days, 23 h 
28 m 15 s, which was fast on apparent time ship 3 m 43 s; dif¬ 
ference longitude 28 m W. since the error was found. Required 
the latitude by reduction to the meridian. 

Long. 


Watch.iod 23h 28m 15s 

Err. fast. — 3 43 



10 

23 

24 32 

Diff. long. W.. 



1 52 

App. T. S_. 

xo 

23 

22 40 

Long, in T. E 


- 7 

53 20 

A. T. G. 

10 

15 

29 20 

Obs. Alt. 


56 ° 

5 i’ 57 ”N 

Dip.. 



4 36 



56 

47 21 

Sun’s corr. 



34 



56 

46 47 

Sem. dia. 

4 


15 58 

True Alt. 


57® 

2’ 45 ” 


D Long. 
28’ W 

4 

6,o)ti,2 
1 in 52s 


T. F. Noon 


118® 20’ E. Decl. N. Incr. 

4 7 q 42 ’ 13” 

- 

6 ,o) 47.3 20 Corr. 14 22 


7h 53m 20s 


7 ^6 35 


23I122 m4os 
24 o o 


H. Var. 
55”-6 


2780 

2780 

556 

6,0)86,1.80 
14’ 22” 


Time F, N.37m 20s 

Lat.23° 40’ 

Decl. 7 0 57’ 

Number. 1201 

T.Alt.57°3’ Nat. sine 83915 
Nat. Cosine.. 


Log. ris. 3 . 12184 
Cosine 9 . 96185 
Cosine 9 . 99581 


Log. 


3 • 07950 


85116 Mer. Z. Dist. 31° 40* S 

Decl. 7 57 N 

Latitude.. 23® 43’ South 
























































































56 


SELF-INSTRUCTOR IN NAVIGATION 


EXAMPLE 3. 


1902, November 23rd, A. M. at ship; Lat. by accouut 
11° 43' N.; Long. 128° 50' W.; observed altitude sun’s lower 
limb south of observer 56° 29* 35" ; eye 19 feet; time by watch 
23 days Oh 56m 10 s, which was fast on apparent time ship 1 h 
34 m 18 s; difference of longitude mnde eastward 14' after the 
error on apparent time ship had been found. Required the 
latitude at noon, ship having made 4' south between noon and 
the time of observation. 


Watch.23d oh 56m 10s 

Err.— 1 34 18 

22d 23I1 21m 52s 

D. Long. E . -f _56 

A. T. IS.... 22d 23h 22m 48 
Long, in T. -/- 8 35 20s 

A. T. G.... 23d 7h 58m 8s 


D. Long. Decl. S. Incr. H. Var. 

14’ 20 q 12’ 51”" 3 I ”-9 

_4 _ Corr. -f- _4 *5 _§_ 

56s Corr. Dec. 20 17 6 6,0)25,5.2 

-= 4 ^ 5 ^ 


Long. 128° 50’ W. 

- 4 A. T. S.23h 22m 48s 

60 ) 5 L 5-20 24 o o 

8h 35m 20s T. F. Noon. 37m 1 2s 


Alt. L. L.56° 29’35” S. 

Corr. Tab. 9 Norie -I- 11 15 
True Alt.56 40 50 


T. F. Noon 37m 12s Log. Ris. 3 . 11873 
Lat. Acc . . ii° 43’ Cosine .. 9.99085 
Corr. Decl. 20° 17’ Cosine . . 9 97220 


Natural Number.1207 Log.3.08178 

T. Alt. 56° 41' Nat. Sine 83565 

Nat. Cosine. 84772 = M. Z. D. 32 0 2’ N. 

Decl. 20 17 S. 
Lat. at sights n° 45' N. 
Diff. Lat. 4 S. 

Lat. at noon n p 41* N. 


EXAMPLE 4. 

1902, October 19th at ship; Lat. by account 35° 
39' N.; Long. 143° 37' W.; altitude sun’s upper limb 44° 9' 
S.; eye 23 feet; time by chronometer October 19th 8h 47 m 
8s; correct mean time Greenwich. Required the latitude at 
noon ; ship ran N. W. x N. 12 knots per hour. 


































REDUCTION TO MERIDIAN 


57 


M.T.G. igd 8h 47m 8s 
Long, in T. — 9 


M.T.S. 

i8d 23I1 12m 40s 

Eq. Time 

- 1 - 14 53 

A.T.S. 

23h 27 m 33 s 
24 0 0 

T. F. Noon 

32m 27s 

Obs. Alt. 

44 ° 9 ' S. 

Dip 

— 4 42 

44 4 18 

Corr. 

— 53 

44 3 25 

Sem. dia. U.L* — 16 5 

True Alt. 

43 ° 47 ' 20" 


Long. 143 0 37' W. Decl. S. incr. 9 0 44' 20" H. Var. 

4 -|- 8 corr. 54.5' 

6,0) 57.4 28 corr. decl. 9 0 5 2' 20" S. 8 8 

9h 34m 28s - * 4360 

- 43^ 

6< o)47«9-6o 

/ 59 - 6 ' 


Equa. Time 

14m 49s 

corr. _4 

14 m 53s 


-||- to M. Time. 


T. F. Noon 32m 27* log ris. 3.00032 
Lat. acc. 35 0 39' cosine 9.90987 

Corr. decl . 9 0 52' cosine 9.99353 
Nat. Number 801.2 Log. 2 . 90372 
T. Alt. 43 0 4/ 20" Nat. sine 692003 

Nat. Cosine 7oooi5=M.Z.D. 45034' 18" N. 
Course N 3 pts. W 6' -5=d. lat. 5.4 Dec l. 9 52 20 S . 

_6 Lat. at Observation 35 0 41' 58" N. 

_ 24 " Diff. Lat. _5 24 N. 

Lat. at Noon 35 0 47' 22 " North. 


EXAMPLES FOR PRACTICE. 


1. 1902, January 4th, P. M. at ship; Lat. by account 
33° 36' N.; Long. 159° 24' W.; observed altitude sun’s lower 
limb south of the observer 32° 57' 45"; eye 15 feet; time by 
watch 4 days, 2 h 47 in 43 s, which was fast 2 h 23 m 30 s on ap¬ 
parent time at ship ; difference longitude made eastward 33 
miles since the error on apparent time was found. Required 
the latitude by reduction to the meridian. 

2. 1902, July 16th, A. M. at ship; Lat. acount 25° 
33' S. ; Long. 63° 25*' E.! observed altitude sun’s lower limb 
42° 39' 25" N.; height of eye 19 feet; time by watch 15 days, 
23 h 55 m 19 s, which was fast 6 m 37 s on apparent time ship; 
difference longitude made west 39 miles since the error was 
determined. Required latitude by reduction to the meridian. 

3. 1902, July 6th, A. M. at ship; Lat account 38° 
38' S. ; Long. 153° 37*' W.; altitude sun’s lower limb 27° 58' 
35" N.; eye 14 feet; time by watch 6 days, 0 h 39 m 24 s, which 
was fast 59 m 34 s on apparent time ship; difference longitude 
made westward 54' after error on apparent time was found. 
Required the latitude by reduction to meridian. 

4. 1902, August 9th at ship; Lat. account 29° 
29' S. ; Long. 84° 37' W.; observed altitude sun’s lower limb 
43° 41' 40" north of observer; eye 22 feet; time by chronom¬ 
eter August 9 d 6 h 4 m 30 s, which was slow 1 m 21 s on mean 
time at Greenwich. Required the latitude 1 by reduction to 
meridian. 

Answers at the end of the Guide. 























LATITUDE BY MERIDIAN ALTITUDE 
OF A STAR. 


If the sextant has an index error, apply it to the altitude 
as read 4- add, - subtract. Then correct for dip by Table 14 
Bowditeh, or Table 5 Norie; always subtract; and refraction, 
Table 20 Bowditeh, or Table 18 Norie. The result will be the 
true altitude. No semi-diameter or parallax are needed. The 
true altitude is now taken from 90° 0' 0" and we have the 
zenith distance, which must be named contrary to the bearing 
of the star when observed, north or south. Now place the star’s 
declination under the zenith distance and if they are both north 
or both south, add them together; but subtract the least from 
the greatest if they have contrary names. The result is the 
latitude, same name as the greater. 

The declination of a star needs no correction, but is taken 
at sight from the Nautical Almanac. It sometimes happens 
that the star cannot be found in the Nautical Almanac by the 
name given in the example. If this is the case, Tables 48 
Bowditeh, or 14 Norie, giving different names for the same 
star, will be helpful. The other name thus found is the one to 
seek for in the Nautical Almanac when taking out the declina¬ 
tion. Table 15 Norie gives one correction for a star’s altitude; 
always subtract. 

EXAMPLE 1. 

1902, February 2nd; observed meridian altitude star 
Sirius was 43° 27' 15" bearing south; eye 24 feet; index error 
+ 0' 45". Required the latitude. 


Obs. Alt. 43 ° 27’ 15” S 

I. E.Jh_ 45 _ 



43 

28 

.0 


Dip 24 ft. 


4 

48 



43 

23 

12 


Ref. for Alt... 

. — 

1 

0 



43 

22 

12' 



90 

0 

0 


Zen. dist . 

. 46 

37 

48 

N 

Star’s decl. 

. 16 

34 

53 

S 

Latitude. 

. 30° 

.2’ 

55 

N 


SHORT METHOD 


O. Alt. 43 ° 2 7 ’X S 

I. E. % 

43 28 

Corr. T. 15 Norie.. . — 5# 

43 22X 
90 o 

46 37 % N 
16 35 S 

Lat . . 30° 2*# N 
























POLARIS 


59 


EXAMPLE 2. 


1902, April 7th; observed meridian altitude star Cano¬ 
pus was 49° 55 f 10", bearing south; height of eye 20 feet; 
index error - 1' 20". Required the latitude. 


Obs. Alt, 

• 49° 

55’ 

10 ” s. 

I. E. 


i 

20 


49 

53 

50 

Dip. 


4 

23 


49 

49 

27 

Ref. 



48 

True A. 

49 

48 

39 


90 

o 

0 

Z. Dist. 

40 

ii 

21 N. 

Stars D. 

52 

38 

31 s. 

Latitude 

12° 

27 ’ 

10” South 


Approx. Shorter Method 
Obs. Alt. 49 ° 55 ’ S. 

I. E. — i 



49 

54 

Tab. isNorie 


5 

T. Alt. 

49 

49 


90 

0 

Z. D. 

40 

11 N 

Decl. 

52 

38 ^ s. 

Lat. 

12° 

27’ South 


EXAMPLES EOR PRACTICE. 

1. 1902, March 29th; observed meridian altitude star 
Algenib 54° 0 r 12", bearing south; eye 22 feet; index error 
- V 15". Required the latitude. 

2. 1902, December 17th; observed meridian altitude 
star An tares 52° 47' 0", bearing north; eye 26 feet; no index 
error. Required the latitude. 

3. 1902, October 15th; observed meridian altitude star 
Castor, bearing north, 64° 17' 55" ; eye 17 feet. Required the 
latitude. 

4. 1902, July 24th; observed meridian altitude star 
Aldebaran, bearing south, was 56° 1' 45"; eye 25 feet. Re¬ 
quired the latitude. 

This last altitude is corrected by Table 15 Xorie. 

Answers cut the end of the Guide. 


LATITUDE BY POLAEIS. 

Several tables are in use, giving corrections for the alti¬ 
tude of this useful little star, in order to get the latitude. Those 
in the Xautical Almanac are splendid, and others are good. 
The table given in this work is considered very useful and com¬ 
plete. 
















60 


SELF-INSTRUCTOR IN NAVIGATION 


We need the sidereal time of observation (right ascension 
of the meridian). 

If Apparent Time at Ship Is Given. To the apparent 
time at ship add the sun’s right ascension, page 1, Nautical 
Almanac, and the result is the right ascension of the meridian. 

If Mean Time at Ship Is Given. To the mean time at 
ship add the sidereal time (page 2, Nautical Almanac), taken 
out for the Greenwich date and accelerated for the hours, min’ 
utes and seconds of the Greenwich time. This gives us the 
sidereal time of observation. 

Note .—The Greenwich time is sometimes given in the 
example; if not given, we must find it before we can accelerate 
the sidereal time, or correct the sun’s right ascension. The 
longitude in time west, added to, east subtracted from the time 
at ship will give the time at Greenwich. 

Correct the observed altitude for index error (if any), dip 
and refraction, to get the reduced altitude (true altitude). 
Table 15 Norie gives one correction for a star altitude, which 
includes dip and refraction. Now, enter the table given on 
page 62 with the right ascension of the meridian, under true 
altitude, and take out the correction, adding to or subtracting 
from the reduced altitude, as that part of the table directs. The 
result is the latitude. 

EXAMPLE 1. 


1902, January 28th, 6h 47 m 14 s A. M. mean time at 
ship; Long. 166° 59' E.; observed altitude of pole star 46° 
64' 20" ; eye 30 feet. Required the latitude. 


M. T. S. 27d i8h 47m 14s 

Long, in Time... — 11 7 56 

Long. E. ' 

166^59' 

4 

Ob*. Alt. 

Dip. 

.... 4 6° 54' 20" 

... — 5 22 

M. T. G. 27d 7 h 39m 18s 

6,0)66,7 56 

Ref. 

46 48 58 


nh 7m 56s 

True Alt 
Corr. from table. 

... 46 48 4 

... 1 5 



t ntitude, 

- 47 ° 5 ? 4 " North 

M. T. S. 27d i8h 47m 14s 

Sid. Time. 27 d =-20 23 19 

Accel. 7h = 1 9 

“ . 3?“= 6 

“ . 18s — 0 

Sid. Time Obs. I5h 11m 48s 




Note. —The above example being 

A. M., we 

add 12 to the 

hours and make the date 

one day less; 

1 this gives 

us astronomi - 






















POLARIS 


61 


cal mean time ship. Then we apply the longitude in time, east 
subtract, to get mean time Greenwich. The sidereal time is 
then accelerated for the hours, minutes and seconds of the 
Greenwich time, and added to the mean time ship to obtain 
sidereal time of observation. 

EXAMPLE 2. 

1902, March 21st, P. M. at ship; Long. 29° 59' W.; 
chronometer, 21 days, 11 h 54m 58s mean time Greenwich; 
observed altitude of star Polaris 64° 59' 50" ; index error +1' 
40"; eye 26 feet. Required the latitude. 

M. T, G. Mar. 2id uh 54m 58 s 
Long. in Tine... — 1 59 56 


Long.W. 

29 ° 5^ 

4 


6 t o) ii,9 56 


xh 59m 56 s 


Obs. Alt... 

64° 

59 ' 

50 " 

I. E. 

-1- 

1 

40 


65 

1 

30 

Table 15 Norie 

— 

5 

18 

Red. Alt. 

64 

56 

12 

Corr. 


44 

O 

Latitude. 

65 ° 

40' 

12" 


M. T. S. 21 9 55 2 

Sid. Time... 2id = 23 52 16 
Accel... uh = 1 48 

“ . 54 m =_ 9 

Sid. Time Obs. 9I1 49m 15s 

Note .—When turning Greenwich time to ship’s time, 
as in this last example, longitude in time east is added, and 
west subtracted. 

EXAMPLE 3. 

1902, January 30th, 6 h 39m P. M., apparent time ship; 
Long. 179° 30' W.; observed altitude Polaris 51° 51' off the 
meridian; eye 28 feet. Required the latitude. 


A. T. S. Jan. 3od 6h 391 
Long, in Time n 58 


A. T. G. 30 18 37 


Long. W. 

1 79 ° 3 ^ 
_ 4 

6,0) 71,8 .0 
11 h 58m 


Sun's R. A. Incr. 
2oh 48 m 34s 

Corr. -I- 3 12 

Red. R. A... 20 51 46 

A. f. S. 6 39 o 


H. Var. 
1 os 
18 


3 


Sid. Time Obs. 3I1 30m 46s 


618 

824 

103 


Obs. Alt.., 
Dip.... 

Ref..... 


. 5i°5i' o" 
. — s 11 


6,0)19,1 .58 

3m I 2 S 


51 45 49 
• — 44 


Red. Alt. 51 45 5 

Corr. — 110 

Latitude. 5o°44 5" North. 

EXAMPLES FOR PRACTICE. 

1902, May 12th, 11 h 0m 30s P. M. mean time ship; 
Long. 113° 2' W.; observed altitude pole star 41° 10' 17"; 
eye 26 feet. Required the latitude. 

1902, September 22nd, 2h 10m A. M. mean time ship; 
Long. 151° 59' E.; observed altitude Polaris 29° 58' 50"; 
index error +3' 10" ; eye 28 feet. Find the latitude. 

Answers at the end of the Guide . v 














































CORRECTION FOR THE ALTITUDE OF STAR POLARIS, FOR THE YEARS 1902, 1903, 1904, 1905 and 1906. 


62 SELF-INSTRUCTOR IN NAVIGATION 


























































































































































LONGITUDE BY STAR. 


The formal rules for working out longitude by star are, 
in many ways, so similar to those of the sun, that very little 
additional explanation is necessary. The longitude is simply 
the difference between the sidereal time at ship and. the sidereal 
time at Greenwich. The pupil should be familiar with mean 
time and sidereal time. 


EXAMPLE. 

1902; suppose mean time Greenwich January 10th 7h 
12 m 14 s, and it be required to find the reduced sidereal time, 
or mean sun's right ascension. Take out from Nautical Alma¬ 
nac, right-hand column, for the Greenwich date, the sidereal 
time at mean noon, as under. 

Jan. ioth Sid. Time 19I1 16m 17s.54 
Accel, for 7I1... = 1 8 .99 

“ 12m.. = 1 .97 

“ 14s .. --_ .04 

Red. Sid. Time. igh 17m 28s.54 

The acceleration is taken from Table 9 Bowditch, Table 
38 Norie, or from the Nautical Almanac. 

Like the ordinary chronometer problem, we need to have 
the mean time Greenwich; the true altitude, latitude and polar 
distance. The star's right ascension and declination are taken 
out at sight from the Nautical Almanac, and require no cor¬ 
rection. 

Add together the true altitude, latitude and polar distance. 
Eind the half sum and remainder; take out the logs, and find 
the hour angle, the same as with the sun. 

Now , Observe. If the star is west of the meridian, add 
the star's right ascension to the hour angle, and you have the 
right ascension of meridian. (You may have to reject 24 
hours.) 

If the star is east of the meridian, subtract the hour angle 
from the star's right ascension, adding 24 hours if necessary, 
and the result is the right ascension of meridian. Or, you may 
turn the eastern hour angle into western hour angle by sub- 






04 


SELF-INSTRUCTOR IN NAVIGATION 


trading it from 24 h, and then treat it the same as star west of 
meridian. 

From right ascension of meridian subtract sidereal time 
(+ 24 h if necessary) and yon have the mean time at ship, which 
must now be dated one day less than the civil date at ship if A. 
M. sight, but the same day if P. M. sight. The difference be¬ 
tween the mean time ship and the mean time Greenwich is the 
longitude in time, which converted in the usual way, will be the 
longitude of the ship; east or west, according as the Greenwich 
time is least or best, thus ending the same as the common chro¬ 
nometer problem. 

The following examples, like many others throughout this 
work, are taken from the author’s own work'book, and com¬ 
puted afresh, using a more recent date. These star observa¬ 
tions, taken under favorable conditions, and otherwise, com¬ 
pare well with the ship’s position by dead reckoning, carried on 
from position by observation at noon. 

EXAMPLE 1. 


1902, January 28tjh, 9 h 0 m P. M. at ship; Lat. 49° 48' 
N.; observed altitude star Procyon, east of meridian, 39° 20'; 
height of eye 26 feet; time by chronometer 27 days, 21 h 25 m 
19 s, which was 1 m 35 s fast on mean time Greenwich. Re¬ 
quired the longitude. 

Chron 2yd 2ih 25m 19s Alt.39 0 20’ 0” Star’s R. A. Star’s Decl. N, 

Err. — 1 35 Dip. .— 50 7b 34m ios 5 0 28’ 34” 

M. T. G.27d 2ih 23m 44s 39 0 15 o” - 9 ° o o 

- Ref.— 1 9 P. Dist.84° 31’26” 

T. Alt.. . 39 ° 13 ’ 5 i” 


Sid. Time on 27d.= 2oh 23m 19s 

Accel, for 2ih.= 3 26 .99 

** for 23m.= 3 .78 

for 44s.=__JT2 

Red. Sid. Time 20h 26m 49S.89 


Alt.39 0 13’ 51s 

Dat.49 48 o Sec.0.190132 

P. D . .. 84 31 26 Cosec.0.001986 

2 )jZ3_33_i7_ 

86 46 38 Cosine.8.750178 

47 32 47 Sine.... 9-867978 

H. Angle E. ih 57m 485=8.810274 

Star’s R. A. 7 34 10 

R. A. Mer. 5 36 22 

Sid. Time. ..20 26 50 

M. T. S. 28d 9 9 32 

M. T. G. 27d 21 23 44 

nh 45m 48s=Xong. it6°2/E 


EXAMPLE 2. 


1902, April 29th, A. M. at ship; Lat. 30° 1/ 10" S.; ob¬ 
served altitude star Altair 25° 25' 20" east of meridian; eye 















































SUMNER 


65 


28 feet; chronometer 28 days, 2h 40in 58 s, which was slow 
3m 5s on mean time Greenwich; index error +0' 30". Re¬ 
quired the longitude. 

Star’s R. A. Star’s DecL 

I9h 46m oa 8° 36' 33" N. 

90 o o 
P. D... 98° 3 6 ' 33 " 


Sid. Time on 28d= 2h 22m 5s .32 
Accel, for 2h= 19 .71 

“ “ 44 «i=_ 7 2 3 

Red. Sid. Time... 2 h 2 2m ;2S 26 


Note .—The logs are taken out to nearest half-minute of 
arc only. 

EXAMPLES FOR PRACTICE. 

1. 1902, August 8th, A. M. at ship; Lat. 49° 2' S.; ob¬ 
served altitude star Fomalhaut 42° V west of meridian; eye 
24 feet; index error - 30"; chronometer 8 days, 2 h 12 m 55 s, 
which was fast on mean time Greenwich 1 m 40 s. Find the 
longitude. 

2. 1902, January 29th, P. M. at ship; Lat. 49° 48' N.; 
observed altitude star Sirius east of meridian 22° 22'; eye 30 
feet; chronometer 28 day, 21 h 28 m 20 s, which was fast on 
mean time Greenwich 1 m 35 s; no index error. Required the 
longitude. 

Note —The logs are all taken out to nearest half-minute 
of arc only. 

Answers at the end of the Guide . 


POSITION BY SUMNER. 

The ship’s position by Sumner is found by assuming two 
latitudes approximating the true latitude, and with these as¬ 
sumed latitudes, finding the corresponding longitude from each 


Chron. 28d 2h 40m 58s 

Slow. -f- 3 5 

M. T. G. 28 2 44 3 


Alt. 25°25 / 20" 

I- E. -/- 30 

25 25 50 

- Dip. — 5 n 

, 25 20 39 

Ref. — 20 

T. Alt... 25 °i8> 39" 

Alt. 25 °i8'39" “* 

Eat. 30 1 10 Sec 0.062542 

P. D 98 36 33 Cosec 0.004920 

2) 153 56 22 

76 58 11 Cosine 9.353181 

51 39 32 Sine 9.894496 

H. A. E . 3h 36m 178= 9 - 3 I 5 I 39 

Star's R. A... 19 46 o 

R. A. Mer.. 16 9 43 

Sid. Time.. 2 22 32 

M. T. S. 28d 13 47 11 

M. T. G. 28d 2 44 3 

n h :im~8 s—Long. 165° 47' East 




































66 


SELF-INSTRUCTOR IN NAVIGATION 


of two separate altitudes, and the chronometer times when these 
altitudes were taken. 

Should the ship remain stationary during the interval be¬ 
tween the observations, the lines joining the positions found 
by each altitude cross at the ship’s position; but if the ship has 
changed her place during the interval, the first line of position 
will have to be carried forward to the end of the run. 

Let the assumed latitudes not be too far apart, nor far from 
the true latitude; for remember that the lines joining the two 
positions obtained from each altitude represent a small part of 
a circle on the earth’s surface of large diameter. If the arc of 
this circle intercepted between the true and assumed latitudes 
is small, it will not differ materially from a straight line. These 
lines of position being small parts of a circle on the earth’s sur¬ 
face from which the sun has the same altitude at that instant, 
the sun must be in the center of that circle, and will bear at 
right angles to the tangent at any point on the circle, and ifhere- 
fore at right angles to the line of position. 

In practice, it is well not to make the second observation 
until the sun has changed its bearing considerably; otherwise, 
the line of position on the chart will cut indefinitely, and 
give an uncertain position. 

RULES. 

1. Take out and correct the sun’s declination and equation 
of time for each Greenwich time of observation. 

2. Find the polar distance at each time of observation, 
and the true altitude of the sun’s center. 

3. Now, with the above, work out four longitudes as in 
the common chronometer question, as follows: 

4. First—Mean time Greenwich and equation of time 
and declination at that time with the first altitude. 

5. Second—Mean time Greenwich and equation of time 
and declination at that time with the second altitude. 

EXAMPLE. 

1902, May 4th, A. M. at ship; time by chronometer May 
3d 22 h 13m 47 s mean time Greenwich; observed altitude 
sun’s lower limb 45° 12' 5". Again, P. M. same day, time by 
chronometer May 4d lh 31m 27s mean time Greenwich; 
observed altitude sun’s lower limb 51° 40' 10"; eye 16 feet; 


SUMNER 


67 


ship’s ran in the interval 34 miles N.E.xE. true. Required the 
line of position at the time of each observation, and also the 
sun’s true bearing, and ship’s position at time of second obser¬ 
vation. Assumed latitudes 51° N. and 51° 30' N. 


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FIRST LONGITUDE SECOND LONGITUDE 


68 


SELF-INSTRUCTOR IN NAVIGATION 


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SUMNER LINES ON THE CHART AND 
SUN’S TRUE BEARING. 


Spot the first longitude in the work and the less assumed 
latitude and mark the place A. Spot the second longitude and 
greater assumed latitude and maik the place B. Connect the 
two by a neat pencil line. This is the line of 'position , and you 
will now note its direction, by sliding the parallel rules to the 
center of the nearest compass, or better still, using Field's paral¬ 
lel rules, you will find the line of position to the nearest degree, 
from one of the meridian lines on the chart. From anywhere 
on this line project another line representing the course and 



distance the ship has gone in the interval bet ween the first and 
second observation, and mark the spot arrived at C. Through 0 










70 


SELF-INSTRUCTOR IN NAVIGATION 


draw a third line parallel to the first line of position. The ship 
will be somewhere on this line. Now, lay off the longitude 
found by the second altitude and less assumed latitude and call 
the place D. Then the longitude found by the second altitude 
and greater assumed latitude and name the spot E. Join D and 
E by a neat pencil line, and the place where this line cuts the 
third line you have made will be the position of the ship at the 
time the second observation was taken. This we will call E, 
and from this point take off the latitude and longitude. 

The sun’s true bearing is always at right angles to the line 
of ship’s position. The bearing will be readily found if we 
remember that, if the ship’s time is A. M., it will be easterly, 
and if P. M., the sun will bear westerly. The line of position 
is taken from 90°, and what remains is the sun’s true bearing. 

Suppose A. M. line of pos. N. 48° E, then the sun’s 

90 

true bearing will be = S. 42 0 E. 

EXAMPLES FOR PRACTICE. 

1. 1902, April 5th, A. M. at ship; chronometer, April 
4 d 22 h 58 m 5 s mean time Greenwich; altitude sun’s lower 
limb 40° 12' 10". Again, P. M., same day; chronometer, April 
5d lh 58m 10s mean time Greenwich; altitude sun’s lower 
limb 42° 21' 40"; eye 22 feet; ship’s run between the sights 
E. N. E. true 30 miles. Required line of bearing and sun’s true 
bearing at time of first observation, and ship’s position when the 
second observation was taken. Assumed latitudes 50° O' N. 
and 51° 0' N. 

2. 1902, October 3rd, P. M. at ship; chronometer, Octo¬ 
ber 3d 12h 38m 10s mean time Greenwich; observed alti¬ 
tude sun’s lower limb 33° 15' 5". Again, P. M., same day; 
chronometter October 3d 14h 52m 3s mean time Green¬ 
wich; observed altitude sun’s lower limb 18° 12' 40"; eye 
16 feet; ship’s run between sights E. N. E. true 22 miles. 
Required line of bearing and sun’s true bearing at time of 
first observation, and the ship’s position at time of second ob¬ 
servation. Assumed latitudes 49° 30' N. and 50° 0' N. 

To avoid unnecessary exactness, the logs in all these ex- 



JOHNSON'S METHOD OF DBL. ALT'S 


71 


amples on Sumner are taken out to the nearest half-minute of 
arc only, which is sufficient for all practical purposes. 

Answers at the end of the Guide . 

JOHNSON’S METHOD OF DOUBLE 
ALTITUDES* 

In the example on Sumner, given in this work, a most 
elaborate display of figures is presented to view, besides the 
accompanying chart work necessary in projecting the Sumner 
lines of position. Of course, it is Sumner pure and simple. 
But, as the same results can now be obtained by an easier 
method, introduced by that mutual friend of mariners, Mr. 
A. C. Johnson, it will be well to give an example or two on 
double altitudes, done according to the more up-to-date method. 
It is not always convenient to project Sumner lines on a chart; 
and a chart of large enough scale is not always at hand. Be¬ 
sides, in the Sumner, the difference in the sun's bearing be¬ 
tween the times of observation must be, say, not less than three 
points, in order to insure anything like good results; whereas, 
with Johnson, half that difference will give splendid results. 
Therefore, to avoid unnecessary trouble, this latter method of 
double altitudes should be practiced, and the whole thing done 
by calculation, from first to last, in this short and approved 
way. The author has used this method for some years, and 
finds it almost indispensable. 

KULE. 

Two observations are taken, with an interval of 1J or 2 
hours between them, provided the sun has altered his bearing 
not less than 2 points. 

Work out the first observation for longitude with the lati¬ 
tude by dead reckoning at the time of observation. Carry on 
this latitude by dead reckoning and the longitude just found, 
for the run the ship has made between the two observations, 
and work the second observation with this new latitude. Name 
the longitudes one and two. The sun's bearing for apparent 
time at each observation must be taken from the azimuth 
tables. 



72 


SELF-INSTRUCTOR IN NAVIGATION 


“Now,” says Mr. Johnson (in his valuable pamphlet en¬ 
titled “Cloudy Weatiher”), “enter Table 1* with the latitude 
and hearings, and take from it two numbers (a) and ( b ), of 
which take the difference, or sum, according as the bearings 
are in the same or different quarters of the compass. The dif¬ 
ference of longitude divided by this difference or sum gives the 
correction for the second latitude and (a) and (&) multiplied 
by the correction for latitude give the corrections for the two 
longitudes.” 

APPLYING THE CORRECTIONS. 

“When the observations are in the same quarter of the 
compass, allow the corrections both to the east, or both to the 
west, in such a manner as to make the two longitudes agree. 
When the observations are in different quarters of the com¬ 
pass, correct the easterly longitude towards the west, and the 
westerly longitude towards the east, in such a manner as to 
make the two longitudes agree . If they do not agree, they 
show that) the corrections have been wrongly applied, and 
herein we have a valuable safeguard against error, peculiar to 
this method only. With either correction and the correspond¬ 
ing bearing, find the name of the correction for the latitude 
thus: Suppose the correction for either longitude to be west, 
and the corresponding bearing S. W.; writing the letters N. E. 
under the above, we see that the letter opposite to W. is N., 
which is, accordingly, the name for the correction for latitude 
two.” 

EXAMPLE 1. 

1902, May 4th, A. M. at ship; time by chronometer 3d, 
22 h 13 m 47 s mean time Greenwich; observed altitude sun’s 
lower limb 45° 12' 5". Again, P. M., same day; time by 
chronometer 4 days, lh 31 m 27 s mean time Greenwich; ob¬ 
served altitude sun’s lower limb 51° 40' 10"; height of eye 16 
feet; latitude by dead reckoning 51° 15' N.; ship’s run be¬ 
tween the observations was 34 miles N. E. x E. true. Re 
quired the latitude and longitude at time of second observation. 

• Table 1 is found in Johnson’s “Cloudy Weather,” a little pamphlet 
every navigator should possess. 




73 


JOHNSON’S METHOD OF DBL. ALT’S 

Note. This is the same example given on page 66 under 
Sumner, and it is here worked by Johnson’s method to show 
the astonishing decrease in figures with the same result. 


FIRST OBSERVATION A. M. 


M. T. G. 

Alt. 

Decl. N. incr 

H. Var. 

Equ. T. incr. 

H. Var. 

3d 22h 13m 47s 

45° 12' 5" 

15 0 28' 32" 

44"-5 

3® 8S.5 

s.28 


- 3 55 

-|- 16 28 

22 .2 

- 1 - 6 .2 

22.2 


45 8 10 

15 45 0 

890 

3m 14s. 7 

1776 


— 51 

90 0 0 

890 

890 

— from app. time 

444 






45 7 19 

P. D. 74 0 15' 0" 

6 v o) 98.7.90 

' 

6.216 

T. Alt. 

~r *5 53 

45° 23' 12" 


16' 28" 




Alt. 45 ° 23 ' 12" 


Lat. 51 

15 0 

0. 203479 

N. E. 


P.D. 74 

15 0 

0. 016619 

N. 5 pts. E. 34' =* 18 9 — 28.3 = 

- 46'tf 

170 

53 12 


51 ° 15 N. 

85 

40 

26 36 

3 24 

8. 900225 

9. 808594 

5 i° 34 ' N. 


H. Ang. 2h 
24 

15m 31s 

.8. 928917 



A.T.S. 3d 21 

44 29 


Sun’s bearing 9h 44m A. M. 

N. 130 0 E- 

Equ.T.— 

3 15 



180 

M.T.S. 3d 21 
M.T.G.3d 22 

41 14 

13 47 



S. 5 o° E. = 1.33 

N. 


Long, in time 32m 33s == Long. 8° 8' 15" W Long, [ij 7 0 22' o" W. 

- d. long. 46 15 E-,. ,Corr. — 4 30 

Long, [x] 7 0 22' o" W. ~ Long." 7 0 17' 30" W. at 2nd obs. 


SECOND OBSERVATION P. M. 


M. T. G. 

Alt. 

Decl. N. incr. 

H. Var. 

Equ. T. incr. 

H. Var. 

4d ih 31m 27 s 

51 0 40' 10" 

15 ° 13 " 

43"-9 

3m 15s 

.26 


— 3 55 

-|- 1 6 

1 -5 


i -5 


51 

36 

15 

15 47 19 

2195 — trom app. time 

130 



40 

90 0 0 

4$9 

26 

51 

35 

35 

P.D. 74 ° 12' 41" 

6,0) 6,5.85 

39 ° 

15 

53 


1’ &' 



T. Alt.. 51 0 51 28 = 

Alt. 51 0 51' 28" 

Lat. 51 34 o .0.206486 Sun’s bearing ih 6m P. M.N 154 0 W 

p. D. 74 12 41 . 0.016709 180 

177 38 9 S 26° W—3.23 

88 49 4 . 8 . 3 U 954 -"^E 

36 57 36 ■ 9 • 779 044 Lat.... 51 0 34' N 

A. T. S. 4d ih 6m 16s . 8.317193 Corr "" 3 30” N 

Equ. T. - 3 15 Corrected Lat. 51 0 37’ 30” North at 2nd obs. 

M. T. S. 413 1 

M. T. G.. 4 i 3 i 27 

Long, in time 28m 26sg== Long. [2] 7 0 6’ 30 W 


11 

Longitude 7 0 iy’ 30” West at 2nd obs. 


(a) 

(*) 


S 50° E = 1.33 Eong. [1] 7 0 22’ .0 
S 26 W = 3.23 Long. [2] 7 0 6’ .5 


4-56 



(a) 

1-33 

3-4 

532 

399 

4-522 


(*) 

323 

3-4 

1292 

969 

10.98a 


1820 






















































































74 


SELF-INSTRUCTOR IN NAVIGATION 


AS PRACTICED DAILY BY THE AUTHOR AT SEA. 

First observation, Thursday, January 30th, 8 h 49 m A. 
M. by clock; Pat. log 65'; eye 30 feet; latitude, dead reck¬ 
oning, 51° 15' N. 


Chron. U. 

Alt. L. L. 

Decl.S. deer. 

H. Var. 

Equ. T. 

incr. 

H. Var. 


3od 8h 51m 51s 

9 °i 3 / o" 

I 7 ° 49 ' 48 " 

40" .7 

13m 23s 

os .42 


Fast — 1 34 

— 5 22 

— 5 58 

8 .8 


4 

8 . 8 

M. T. G.. 

,. 3od 8h 50m 17s 

9 7 38 

17 43 50 

3256 

13m 27s 

336 



— 5 34 

90 0 0 

3256 

. , - 

. - 

336 



Q 2 4 

I 07 ° 43 ' 50 " 

6,0) 35,8.16 

~/“tO Hpp, 

.time 

3«696 



16 15 


5 ' 58 " 





1 

\Alt.9°i8'i9" 





Alt. 

. 9°i8'i 9 " 

N. 

75 ° E. 18'= 

4 . 7 - 17-4 = 



28' E 

Lat. 

. 51 15 0 —203479 Eat. [1] 51 0 15'N. 


177 

10 45 W 


P. D .107 43 50 — 021142 

168 17 9 

84 8 34 9 . 008894 


Eat [2] 51 0 iq' 42" 


74 50 15 9 • 
A.T.S. 29d 2oh 48m 7s 9 , 
Equ.T. -f- 13 27 
M.T.S. 29 21 1 34 

M.T.G. 3 0 8 50 17 

nh 48m 43s 


984603 

218118 

Long. i77°io'45” 

a8 

Long. [1] 170 42 45 
Corr. 14 o 


Long. [1] r76°42 / 45 / ’ W 


Sun’s Azim. N 134 0 E 
180 

S 46 E=i .53 

N Ss --- W 


65’ 


Longitude 176° 56' 45" West. 

Second observation, about 10 h 32 m A. M. Log 83’— 
= 18’ N. 75° E. 


Same Chron. 

3od ioh 33m 36s 

Fast. —_ 1 34 

M.T.G... 3od ioh 32m 2s 


Alt. L. E- Decl.S. deer. 


Alt... 

... 18 0 

' 23 ' 

9 ' 


Lat.. 

- 5 i 

19 

42 

— 

P. D. 

.. 107 

42 

41 

— 


177 

25 

32 



88 

42 

46 



70 

19 

37 


A. T. S... 

... 29d 

22h 

33m I3S«= 

Equ. T... 

- * ( 


13 

27 

M. T. S.. 

... 29 

22 

46 

40 

M.. T G.. 

... 30 

IO 

32 

2 


i8°i5 / o" 

— 522 
18 9 38 

— 2 44 

18 6 54 

16 15 

T.Alt.i8°2 3 '9" 


204188 

021O82 


8 .350181 
9.973875 

8.549326 


I 7 ° 49 ' 48" 
— 17 
17 42 41 
90 o o 

I07 0 42'4i" 


H. Var. Equ. T. incr. H. Var. 
40" .7 13m 23s os .42 

«> -5 _4 10 .5 

2035 13m 27s 210 

= 

/ 7" 


Sun’s Azim. C N 158° E 

180 

SV22 E= 3»94 

N --nW 

Eat. [a] 51 0 19' 42" N 

9 12 S 


Corr... 
Latitude.... 


51° 10' 30" North. 


(a) 

(*) 


nh 45m 22s = Long. [ 2 ] 176° 20' 30" W 
Corr. 36 15 W 
Longitude 176° 56'45" West. 
76 ° 42' .75 ( a ) 

176 20 .50 
22 


S 46° E = 1.53 Long, [1] 1 
S 22 E = 3-94 Long. [2 1 1 
2.41 


)! 


J( 

560 


9.2 


1.53 

9-2 

306 

1377 

14,076 




3-94 

_ 9-2 

788 

3546 

36,248 


Logs are taken out to nearest half min. of arc. 

EXAMPLE FOE PRACTICE. 

1902, January 27th, 9h 20m A. M. by clock; latitude 
by account 46° 44' N.; chronometer 26 days, 10 h 32 m 7 s 














































































STAR TIME AZIMUTH 


75 


mean time Greenwich; altitude sun's lower limb 14° 15'. 
Again, same day, about 10 h 46 m A. M.; chronometter 26 days, 
12h 4m 18s mean time Greenwich; altitude sun’s lower 
limb 22° 11'; eye 28 feet; ship’s run between sights N. 63° 
E. 12 miles. Required latitude and longitude at time of 
second observation, by Johnson’s method. 

Answer at the end of the Guide. ■ 


STAR TIME AZIMUTH. 

We need the Greenwich time, which may be given in the 
example, but if not given, we must find it by applying the longi¬ 
tude in time; west add; east subtract; for the purpose of ac¬ 
celerating the sidereal time for the hours,, minutes and seconds 
of the Greenwich date. 

If mean time at ship is given, make it astronomical mean 
time at ship, and to it add the accelerated sidereal time to get 
the right ascension of meridian. From this subtract the star’s 
right ascension, and the result is the hour angle west. If it is 
more than 12 hours, take it from 24 hours and name the re¬ 
mainder hour angle east. 

If apparent time at ship be given, then, to the astronomi¬ 
cal apparent time at ship add sun’s right ascension and the re¬ 
sult is right ascension of meridian, from which we subtract 
the star’s right ascension to get the hour angle west. Should 
it exceed 12 hours, subtract from 24 hours and call result hour 
angle east. 

Enter the azimuth tables with nearest degree of latitude 
and declination, and the hour angle to nearest minute in the 
P . M. column. Take out the star’s true azimuth and name it 
north or south, as directed at the foot of the page, and east or 
west, as the hour angle is east or west. Then proceed to find 
the compass error and deviation, as with the sun’s azimuth. 

Note .—In each case add 24 hours or reject' 24 hours, if 
necessary. 

EXAMPLE 1. 

1902, May 10th, 3 h 10m A. M. mean time at ship; lati- 



76 


SELF-INSTRUCTOR IN NAVIGATION 


tude 60° 5' N.; longitude 31° 12 ' E.; compass bearing of 
star Areturus S. 56° 15' W.; variation 12° 7' E. Required 
compass error and deviation by time azimuth tables. 




Long. E. 

M.T.S. 9d 15I1 

10m 

31 0 12’ 

— 2 

5 

4 

M.T.G. 9 13 

5 

60)124 48 



2h 4m 48s 

True Azim. N. 

io5 q 

15 ’ W. 


180 


True.S 

74 

45 W. 

Comp.S 

56 

15 w. 

Error. 

18 

30 E. 

Var. 

12 

7 E. 

Deviation. 

6° 

23 ’ E. 


Star’s decl. 

19 ° 4 i’ 33 ’ 1 N. 

Star’s R. 
I4h 11m 

A. 

IIS 

Sid. Time 9th 

= 3 h 

5 m 

27s 

Accel, for 13I1 


2 

8 

Accel, for 5m 

= 


1 

Red. Sid Time 

3 k 

7m 

36s 

M. T. S. 

15 

IO 

0 

R. A. Mer. 

18 

17 

36 

Star’s R. A.. .. 

14 

11 

11 

Hour Angle W. 

4 h 

6m 

25s 


EXAMPLE 2. 

1902, October 21 st, 11 h 10 m P. M. mean time ship; 
Lat. 31° 10 ' S.; Long. 123° 4' W.; star Algenib bore by 
compass N. 52° 55' W.; variation 13° 59' E. Required 
compass errror and deviation. 


d h m 

M. T. S. 21 ii io 

-J- 8 12 16 
d h m s 
M. T. G. 2i 19 22 16 


Long. 123 0 4’ W 
_4 


Star’s decl. I4°38 , i9” N 


h m s 
Star’s R.A. o 8 n 


6,0 )49,2 16 


Sid. Time... 2ist=i3h 55m 59s 
Accd. for.... iqh= 3 7 

“ “ ... 22m== 4 


Red. Sid. Time 13I1 59m 10s 


8h 12m 16s 


T. Azim. S i6o°W 
M. T. S. nh 10m os 180 


Sid. T... 13 59 10 


R.A. Mer. 1 9 10 

Star’s R. A., o 8 11 


H. A. W. ih om 59s 


True N 20 W 
Comp. N 52°55’W 


Error 

Var... 


32 55 E 
13 59 E 


Variation i8°56’ E 


EXAMPLES FOR PRACTICE. 

1. 1902, October 20th, 4h 2 m A. M. apparent time at 

ship; Lat. 54° 54' S.; Long. 96° 56' E.; star Sirius bore by 
compass N. 3° 40' W.; variation 9° 50' E. Required compass 
error and deviation by the azimuth tables. 

2 . 1902, January 18th, 7h 5 m 30 s mean time Green¬ 

wich; Lat 39° 48' S.; Long. 21 ° 10 ' E.; star a Arietis bear¬ 
ing N. 35° 30' W. by compass; variation 13° 10 ' E. Find 
the error of compass and deviation by the time azimuth tables. 

Answers at the end of the Guide. 

(For Lat. by Mer. Alt. of the Moon, see page 117 .) 





















































ON THE CHART. 


The Sides of a Chart. The north side of a chart is usu¬ 
ally known by a decoration of some kind at the north end of 
the needle of any compass printed thereon. Letters and figures 
are generally printed with their heads toward the north. In 
using the chart, therefore, the north side is to be considered 
the top, the right-hand side east, the left west, and the bottom 
south. See to this when a strange chart is placed before you, 
before attempting to use it. 

Meridians. The lines running due north and south are 
called, meridians. The side meridians marked with degrees 
and minutes are called graduated meridians, and are used for 
measuring latitude and distance. 

Parallels. The lines running east and west are called 
parallels of latitude. Those at the top and bottom marked with 
degrees and minutes are termed graduated parallels, and are 
used for measuring longitude. 

Latitude. To tell the latitude of a place we must see the 
degree or degree and minute at the side directly opposite the 
place. To spot a given latitude on the chart, we must see that 
we put the position directly opposite the latitude given. If the 
latitude degrees increase upwards, the latitude is north, and the 
chart represents part of the northern hemisphere. If the lati¬ 
tude degrees increase downwards, the latitude is south, and the 
chart represents part of the southern hemisphere. 

Longitude. To tell the longitude of a place, we must see 
the degree or degree and minute at the top or bottom directly 
above or below the place. To spot a given longitude on the 
chart, we must see that we put the position directly above or 
below the longitude given. Longitude increases from 0° to 
180°. When the degrees of longitude on a chart increase 
toward the right, the longitude is east; but if they increase to 
the left, the longitude is west; and this rule applies in both 
hemispheres, the top of the chart being north in both cases. 
If the meridian of Greenwich, longitude 0°, is on your chart, 


78 


SELF- INSTHUCT.011 IN NAVIGATION 


the longitude to the right of it will be east, and to the left west 
longitude. If the 180° meridian is on your chart, the longitude 
to the right of it will be west, and to the left east. 

Latitude and Longitude Given to Spot Position on Chart. 
Lay the edge of the parallel rules along the parallel of latitude 
on the chart next below the latitude given. Slide them up, 
preserving their direction, till they reach the exact latitude 
given. Now take the given longitude in the dividers from the 
top or bottom, fix one leg on a meridian near the given longi¬ 
tude and the other on the longitude along the edge of the paral¬ 
lel rules, exactly as it was taken from the top or bottom of the 
chart. Where the second leg falls will be the ship’s position. 

Finding the Course Between Two Places. Lay the edge 
of the parallel rules over the places; slide the rules (retaining 
their direction) to the center of the nearest compass, and there 
read off the course, true or magnetic, as the chart compass is 
true or magnetic. 

Measuring the Distance . Take half the distance between 
the places in a pair of dividers, place one leg on the side of the 
chart at the middle latitude of the places and count the miles 
the other leg will reach north and south. This will be the re¬ 
quired distance. 

Find the Latitude and Longitude of a Given Spot on the 
Chart. Lay the edge of the rules along the parallel of latitude 
next below the given spot, so that if possible, the ends will 
reach the graduated meridian at the side. Now slide the rules 
till they touch the given spot. The latitude may now be read 
from the side of the chart, and the longitude must be measured 
with the dividers along the edge of the parallel rules, and trans¬ 
ferred for reading, to the graduated parallel directly above or 
below. This is called Finding the Position. 

Laying Off Bearings. Lay the edge of the rules over the 
center of the nearest compass touching the bearing given. Slide 
the rules carefully, preserving their direction, till the edge is 
over the given point, and project a faint, line along the edge out 
from the point, opposite to the bearing. The ship is some¬ 
where on that line, and if we lay off the bearing of some other 
point in the vicinity, considerably angled to the first, then 


ON THE CHART 


79 


where the second line cuts the first, will be the position of the 
ship. 

Notes. The small numbers placed about a chart indicate 
the depths of water in fathoms, unless otherwise stated, at low 
water ordinary spring tides; and the small letters show the 
kind of bottom. The Roman numerals occasionally seen on 
charts, near the coasts, and in harbors, indicate the time of high 
water at full and change of the moon at that place; and in the 
absence of any special tables, the approximate time of high 
water can be obtained by these numerals as follows. Add to the 
chart numerals 49 minutes for every day elapsed since full or 
change of the moon, and the sum will be the P. M. high water 
approximately, for that day. 

When a strange chart is placed before you, be prompt to 
notice whether the compasses printed thereon are true or 
magnetic. On some charts, both are combined. The north and 
south lines of a true compass will run parallel with the meri¬ 
dians, but the north and south line of a magnetic compass will 
be more or less angled to the meridians, depending on the 
amount of local variation; and where no variation exists, the 
north and south line of a magnetic compass will, like the true 
compass, run parallel with the meridians. 

When a magnetic course is taken from the chart, the devi¬ 
ation, if any for the direction of the ship’s head must be 
applied, in order to obtain the course to steer by the ship’s 
compass, allowing easterly deviation to the left, and westerly 
to the right; the very opposite to what you would do when 
allowing the deviation on a compass course or bearing to get 
the magnetic. 

When a true course is taken from a chart, the local varia¬ 
tion must be allowed, easterly to the left and westerly to the 
right; this will give the magnetic course; and, if there is no 
deviation, this will be the course to steer by the compass; but 
if deviation exists, as in all likelihood it will on iron vessels, 
this, too must be allowed before we have the proper compass 
course. Remember that variation and deviation are allowed 
the same way. Easterly variation allowed to the left and 
westerly to the right brings a true course to a magnetic course 


80 


SELF-INSTRUCTOR IN NAVIGATION 


and in like manner easterly deviation allowed to the left, and 
westerly to the right, brings a magnetic course to a compass 
course. 

A compass couse, or bearing needs correcting for devia¬ 
tion (if any) to make it magnetic; easterly to the right and 
westerly to the left; and if we want to bring it to a true course, 
or bearing, we must also allow the variation, easterly to the 
right, westerly to the left. When a true course is found by 
Mercator’s sailing, we must allow the variation and the devia¬ 
tion (if any) to reduce it to a compass course, in the same 
manner as if it were a true course taken from the chart, east¬ 
erly to left, westerly to right, as shown above. 


GREAT CIRCLE SAILING. 

Without going into the principles of Great Circle sailing, 
or showing figures enough in the computation of this valuable 
problem, to make the ordinary, every-day navigator “say 
things,” the writer has thought it more to the purpose,to intro¬ 
duce, in this part of the work the late Professor Airy’s short 
and useful method for sweeping an arc of a Great Circle on a 
Mercator’s chart, which includes the neat little table shown 
below. 

RULE. 


1 . “Join the two points, between which it is required to 
project the Great Circle, by a straight line. Bisect this line, 
and from the point of section erect a perpendicular to the line 
on the side next the equator, continuing it if necessary beyond 
the equator.” 

2 . “With the middle latitude (between the two places) 
enter the following table, and take out the ‘corresponding par¬ 
allel.’ ” 

3. “The center of the arc of the Great Circle, required 
to be drawn, will be the intersection of this parallel with the 
perpendicular ” 



















































































































































































CURRENT SAILING 


81 


Professor Airy’s table for drawing arcs of Great Circles 
on a Mercator’s chart: 


Middle I/at. Corr. Parallel. 


20°. 

f 8i° 13’ 

22 . 

78 16 

24 . 

3 74 59 

26 . 

.5 71 26 

28 . 

a. 67 38 

30 . 

*3 63 37 

32 . 

^ 59 25 

34 . 

* 55 5 

36 . 

14 5° 36 

38 . \ 

3 46 0 

40 . 

<D 41 l8 

42 . 

| 36 31 

44 . 

a 31 38 

46 . 

1) 26 42 

48. 

*55 21 42 

50 . 

& 16 39 

52 . 

& 11 33 

54 . 

^ 6 24 

56 . 

1 x 3 


Middle Lat. Corr. 


58 ° 

60 

62 

64 

66 

68 

70 

72 

74 


76 

78 


80 




tn 

cO 

V 

a 

c3 

c 

4 J 

a 

03 


Parallel. 


4° 

0’ 

9 

15 

14 

32 

19 

50 

25 

9 

30 

30 

35 

52 

4i 

14 

46 

37 

52 

1 

57 

25 

62 

5i 


Navigators are grateful to the late Prof. Airy for these 
rules and table, which are considered the best known on the 
subject. 


CURRENT SAILING. 

Steering to Counteract a Known Current. Spot the 
ship’s position on the chart, and from this point draw a pencil 
line representing the course you wish to make good, from the 
same position point, draw another line in the direction the cur¬ 
rent sets, also mark the distance it will set in one hour on this 
line; take in the dividers the distance the ship will travel in 
one hour, place one leg at the mark on the current line, and 
mark the spot where the other leg will fall on the course you 
wish to make good: a line joining these two marks will be the 
course on which to keep the ship to counteract the current. If 
a magnetic course, it must be corrected for deviation to make 
it a compass course. 

Example. Let S in the diagram represent the ship’s po¬ 
sition. D her destination, and the line connecting these the 
course to be made good. Lay off from S the rate and set of 
current per hour and call this C; then take in the dividers the 





































82 


SELF-INSTRUCTOR IN NAVIGATION 


run of the ship for one hour; place one leg at C and mark the 
spot F where the other leg falls on the line S-D. A line join¬ 



ing C and F will represent the true course to steer to make geo I 
the course intended. 


DEFINITIONS. 

The applicant for his first ocean license may be required to 
give in writing a number of the following definitions, accord¬ 
ing to the discretion of the inspector: 

1. The Equator. The great circle supposed to be drawn 
round the earth 90° from the poles. 

2 . The Poles. The ends of the axis of the earth. 

3. A Meridian. A great circle passing through the 
poles, cutting the equator at right angles. 

4. The Ecliptic. The great circle which the sun ap¬ 
pears to describe annually in the heavens. 

5. The Tropics. The parallels of latitude about 23° 
28' north and south of the equator. 

6 . Latitude. The distance of any place north or south 
of the equator, measured on a meridian. 

7. Parallels of Latitude. Smaller circles parallel to the 
equator. 

S. Longitude. The distance of any place east or west of 
the first meridian, measured on the equator. 

9. The Visible Horizon. The circle where the sea and 
eky appear to meet. 

10 . The Sensible Horizon. The plane touching the 







DEFINITIONS 


83 


earth where the observer stands, and extending to the heavens. 

11 . The Rational Horizon. The plane passing through 
the center of the earth parallel to the sensible horizon. 

12 . Artificial Horizon and Its Use. A reflector, the sur¬ 
face of which is perfectly level. It is used for observing alti¬ 
tudes. 

13. True Course of a Ship. The angle between the 
ship’s track and the true meridian. 

14. Magnetic Course. The angle between the ship’s 
track and the magnetic meridian. 

15. Compass Course. The track of a ship as shown by 
the compass. 

16. Variation of the Compass. The angle between the 
true and magnetic meridians. 

17. Deviation of the Compass. The deflection of the 
compass needle to the right or left of the magnetic meridian. 

18. Error of Compass. The deflection of the compass 
needle to the right or left of the true meridian. 

19. Leeway. The angle between the ship’s track 
through the water and her fore and aft line. 

20 . Meridian Altitude of a Celestial Object. The angu¬ 
lar height of an object above the horizon when it is on the me¬ 
ridian. 

21 . Azimuth. The arc of the horizon between the north 
and south points, and a vertical circle passing through the 
object. 

22 . Amplitude. The arc of the horizon between the 
east point and the object when rising, or the west point and the 
object when setting. 

23. Declination. The distance of an object north or 
south of the heavenly equator. 

24. Polar Distance . The distance of an object from the 
pole of the observer. 

25. Right Ascension. The angle at the pole between the 
meridian passing through the object and the meridian passing 
through the first point of Aries. 

26. Dip or Depression of the Horizon. The depression 
of the visible horizon below the level of the sensible horizon. 


84 


SELF-INSTKUCTOR IN NAVIGATION 


27. Refraction. The bending of the rays of light as 
they pass through the atmosphere. 

28. Parallax. The angle at the center of a heavenly 
object subtended by the radius of the earth at the position of 
the observer. 

29. Semi-diameter. The angle at the eye of the observer 
subtended by the radius of the object. 

30. Augmentation of the Moons Semi-diameter. The 
difference between the semi-diameter when observed in the 
horizon and when in altitude. 

31. Observed Altitude. The angular height of an ob¬ 
ject as observed with an instrument. 

32. Apparent Altitude. The observed altitude cor¬ 
rected for dip and semi-diameter. 

33 . True Altitude. The angular height of the center of 
an object above the rational horizon. 

34 . Zenith Distance. The arc of a vertical circle be¬ 
tween the object and the zenith of the observer. 

35. Vertical Circles. Great circles passing through the 
zenith, cutting the horizon at right angles. 

36. Prime Vertical. The vertical circle passing through 
the east and west points of the horizon. 

37. Civil Time. Time in common use; the day com¬ 
mencing at midnight and terminating at the following mid¬ 
night. 

38. Astronomical Time. Time used in astronomical 
calculations; the day commencing at noon and terminating at 
the following noon. 

39. Sidereal Time. The westerly hour angle of the first 
point of Aries. 

40. Mean Time. The westerly hour angle of the mean 

sun. 

41. Apparent Time. The westerly hour angle of the 
true sun. 

42. Equation of Time. The difference between mean 
and apparent time. 

43. Hour Angle of a Celestial Object. The angle at 
the pole between the meridian of the observer and the meridian 
passing through the object. 


DEFINITIONS 


85 


44. Compliment of an Arc or Angle. The difference 
between the arc or angle and 90°. 

45. Supplement of an Arc or Angle. The difference 
between the arc or angle and 180°. 

46. Great Circles. Any circle which divides a sphere 
into tw T o equal parts. 

47. Vertex of a Great Circle. That part of the great 
circle farthest from the equator. 

48. Small Circles. A circle which divides a sphere into 
two unequal parts. 

49. Right Angle. The inclination of two lines, one 
perpendicular to the other, meeting at a point = 90°. 

50. Oblique Angle. Any angle except a right angle. 

51. Obtuse Angle. Any angle exceeding 90°. 

52. Arc. A portion of the circumference of a circle. 

53. Equinoctial. Celestial equator; it is the earth's 
equator extended to the celestial concave. 

54. Difference of Latitude. The distance a ship sails 
north or south. 

55. Meridional Parts. The length of the enlarged me¬ 
ridians on a Mercator’s chart in miles of the equator for every 
minute of latitude. 

56. Departure. The distance in nautical miles that a 
ship sails true east or west. 

57. Nautical Mile. The mean length of a minute of 
latitude = 6080 feet. 

58. Rhumb Line. The shortest line which can join 
tw r o places, cutting all the meridians at the same angle. 

59. Prime Meridian. The Standard Meridian, from 
which longitude is measured. 

60. First Point of Aries. The point where the sun cut3 
the equinoctial passing from south to north. 

61. Radius. Half the diameter. 

62. Elevated Pole. Pole nearest the observer. 

63. North Magnetic Pole. The point to which the north 
end of the compass needle is directed, situated in Lat. 70° N r . 
and Long. 97° W. 

64. South Maanetic Pole. The point to which the south 


86 


SELF-INSTRUCTOR IN NAVIGATION 


end of the compass needle is directed, situated in Lat. 74° S. 
and Long. 147° E. 

65. Polaris, or Pole Star. The *tar which appears 
nearest to the true north point of the heavens; it is situated 
1° 15' from the celestial pole. 


ADJUSTMENTS OF SEXTANT. 

1 . What is the first adjustment of the sextant ? 

To set the index glass perpendicular to the plane of the in¬ 
strument. 

2. How is that adjustment made? 

Place the index near the middle of the arc, hold the in¬ 
strument face up and arc from you, look into the index glass, 
and if the true and reflected parts of the arc form one continu¬ 
ous line the index glass is perpendicular; if not, make it so 
by screws at the back of the index glass. 

3. What is the second adjustment? 

To set the horizon glass perpendicular to the plane of the 
instrument. 

4. How do you make that adjustment? 

Fix the index at nothing hold the instrument nearly hori¬ 
zontal, face up, look through the horizon glass at the horizon, 
and if the true and reflected parts of the horizon form one 
line the glass is perpendicular; if not, make it so by the upper 
screw at the back of the horizon glass. 

5. What is the third adjustment? 

To set the horizon glass parallel to the index glass when 
the index is at nothing. 

6 . Describe how you make the third adjustment. 

Fix the index at nothing, hold the instrument vertically, 
look through the horizon glass at the horizon, and if the true 
and reflected parts of the horizon form one unbroken line, the 
horizon glass is parallel to the index glass; if not parallel, make 
it so by the lower screw at the back of the horizon glass. 

7. How would you proceed if a screw be lost or broken ? 

I would find the index error. 



ADJUSTMENTS OF SEXTANT 


87 


8 . How would you find the index error by the horizon ? 

Clamp the index near nothing, hold the instrument verti- 

eally, look through the horizon glass at the horizon, and bring 
the true and reflected parts of the horizon into one continuous 
line by moving the tangent screw. The reading now is the index 
error, to be added, if off the arc; but subtracted, if on the arc. 

Note .—The inspector may desire the applicant to answer 
ihe above in writing. He will also make a practical test of the 
applicant in the matter of reading and setting the sextant to 
any given angle. 

Applicants for a high-grade license may be required to 
state in writing. 

9. How do you find the index error by the sun ? 

Clamp the index at about 30 minutes off the arc, hold the 

instrument vertically, and look at the sun; two suns will now 
appear, one above the other, the edges of which I must bring 
together by means of the tangent screw, and mark down the 
reading. Move the index to about 30 minutes on the arc, and 
bring the suns into contact again and note the reading. Sub¬ 
tract the less reading from the greater and divide the remainder 
by 2, the result is the index error to be added if the greater 
reading is off and subtracted if the greater reading is on the 
arc. 

EXAMPLE. 

First reading 34’. o” off the arc. 

Second reading ^! .0 on the arc. 

2) 3>-o 

Index Error i^o” to add. 

10. Have you any proof that these angles have been taken 
with reasonable accuracy? 

Yes; the sum of the two readings divided by 4 should 
equal the sun’s semi-diameter for the day the angles were 
taken as given in the Hautical Almanac. 

EXAMPLE. 

Firtt reading 34 ’•o’* 

S«sond reading 31 .0 

4)65 .0 

Semi diameter 16’ 15” 









88 


SELF-INSTRUCTOR IN NAVIGATION 


THE LOG LINE. 

The length of a knot in feet should bear the same proportion to 
the number of feet in a nautical mile that the seconds run by the 
glass do to the seconds in an hour. 

Rule.—M ultiply the feet in a nautical mile by the seconds rue 
by the glass, and divide by the seconds in one hour. 

A nautical or geographical mile contains 6,080 feet. 

Example. —Find the length of a knot corresponding to a 28 
seconds glass: 

6080 feet in a nautical mile. 

_28 seconds glass. 

48640 

12160 

Secs, in 1 hr. 3600 >170240(^7 feet 
14400 — 

26240 

25200 Ans. 47 feet 3# in. nearly 

1040 

_12 inches in a foot 

3600 )i248o( inches nearly 
10800 — 

1680 

Short Rule. —Annex a cypher to the seconds run by the glass 
and divide by six; the result is the length of a knot in feet. Mul¬ 
tiply the remainder (if any) by 2 for inches. 

Example. —What is the length of a knot for a 30 seconds glass 
by the short rule ? 


6)300 
_ 50 feet 

Find the length of a knot corresponding to a 20 seconds glass 
by the long rule : Ans. 33 feet 9 inches nearly. 

What is the length of a knot corresponding to a 30 seconds 
glass by the long rule? Ans. 50 feet 8 inches. 

Find the length of a knot for a 26 seconds glass by the short 
rule : Ans. 43 feet 4 inches. 

What is the length of a knot for a 28 seconds glass by the short 
rule ? Ans. 46 feet 8 inches. 











THE LEAD LINE 


89 


THE LEAD LINE. 


The Hand Lead Line has “9 marks and n deeps.’* 
The marks are as follows: 


A.t 2 fathoms the mark is 

“ ^ (( n «< 

<< q «< << <( 

“ y i( <« •( 

<( JQ (« «< (« 

<« <« <( «t 

(( j- ti <« (I 

<1 jy (« < ( «( 

<< 20 ** ** “ 


.Leather with two ends. 

. Leather with three ends. 
.White rag. 

.Red rag. 

Leather with hole in it. 
. Blue rag. 

.White rag. 

Red rag. 

.Cord with two knots. 


The Deep-sea Lead Line is marked the same as far as 20 
fathoms, then, a piece of cord with an additional knot at every 
10 fathoms; and apiece of cord with a single knot at every 5 
fathoms between the tens. 


DISTANCES OFF LIGHTHOUSES. 

To find the approximate distance from a lighthouse or 
other object when steering along a coast. 

Rule. Note the bearing of the object, the time by watch, 
and the difference between the bearing and the ship’s course; 
continue on the course until the object’s bearing has altered as 
much again as the difference noted. The distance from the 
object will now be equal to the run of the ship in the interval, 
making allowance for any known current or tide. 

Example. 10 P. M., steamer going north by compass 12 
knots an hour. Cape Flattery light bore N. E. x N. J N. The 



difference between this and the course north is 2J points. We 
continue on the course until 10 h 30 m P. M. when the light 






















90 


SELF-INSTRUCTOR IN NAVIGATION 


bears K. E. x E., or five points from the course. The distance 
off the lighthouse will now equal the distance run in the interval 
of one-half an hour between the bearings, namely six miles. 

The course and bearings are magnetic. 

Four Point Bearing. Note the reading of the log when 
the object is four points on the bow; continue on the same 
course, noting the log again when the object is abeam. The dis¬ 
tance the ship has traveled in the interval will be the distance 
off. Or, knowing the rate of speed, the watch may be used in¬ 
stead of the log. This method is useful when taking a depart¬ 
ure, but does not tell the distance off until you are abeam of the 
object. 

The following method will give timely warning when ap¬ 
proaching an object beset with outlying dangers. 

Rule .—Haul the light, or day object exactly abeam, head¬ 
ing off, keep that course strictly until the light, or other object 
is exactly one point abaft the beam; now, the distance the ves¬ 
sel has gone in the interval, multiplied by five, will be the ap¬ 
proximate distance from the light, on the last bearing. You 
may now set a safe course. The accompanying diagram shows 
the course of a ship approaching the strait of Juan de Fuca in 
hazy weather. She is steering N. E. magnetic, and suddenly 
Cape Flattery light heaves in sight bearing E. N. E., but the 



distance off is a conundrum. Knowing this rule he hauls N. N. 
W., bringing the light right abeam.; he steers thus until the light 
bears E. x N.; he knows his vessel’s speed to be 10 knots, and 







SOUND AND ECHOES 


91 


it has taken just three minutes to change the bearing of the 
light one point, therefore, he has traveled just half a mile; and 
5 tim^ps -J a mile make 2J miles, the distance from the light 
when it was one point abaft the beam. He now sets a safe 
course N. N. E., passing about two miles off the light; whereas, 
the original course if continued, would have carried him on to 
Duntze Rock. 

Note .—In the above cases, the navigator is not. required 
to leave the bridge, or quarter-deck, to obtain his position, but 
when his position is known by the rules, he may then consult 
his chart for a new course, if necessary. The diagrams are 
simply given to prove the methods. 


SOUND AND ECHOES. 

Distance by Sound. Sound travels at the rate of 1090 feet 
per second when the air is at freezing point, or 32° Fahrenheit; 
and this rate is increased by 1.19 feet for every degree above 
that temperature giving 1123 feet (or 374 yards) per second 
at a mean temperature of 60°. This may be used for all ordin¬ 
ary purposes. 

Example :—The flash of a gun was seen at 12 h om i s. 

The report was heard at 12 o 10 

9sT 

374 X 9 = 3366 yards. 

Or by acceleration, thermometer at 85° Fahrenheit. 

85° at 32 0 Sound travels 1090 feet per second. 

32 1.19X53= _ 6 3 

Diff. 53 0 at 85° Sound travels 1153 feet per second. 

1153 X 9 = io 377 feet, or 3456 yards. 

A good way to measure distance by sound is first by 
knowing the number of beats your watch gives in one minute. 
This can readily be ascertained by holding the watch close to 
the ear and watching with the eye a complete revolution of the 
second hand of a chronometer, at the same time counting the 
beats by the watch; 150 beats is common with good watches, 
or 5 beats in 2 seconds. Now, at 60° Fahrenheit, sound travels 
150 yards in one beat of a watch beating 150 times per minute, 
therefore, that number of yards multiplied by the number of 




92 


SELF-INSTRUCTOR IN NAVIGATION 


beats between flash and report will be the distance from the gun. 

Whistle Echoes From Land. We will suppose a mean tem¬ 
perature of 60° Fahr., at which sound travels 1123 feet per 
second. The echo returns in 5 seconds after the whistle com¬ 
menced to sound. If we multiply 1123 feet by 5 seconds we 
have 5615, the number of feet the sound has covered in its 
round trip. Divide this by 2 and we have 2807 feet, or nearly 
half a mile, the distance off that part of the land from whence 
the echo came. 


UNIFORM SYSTEM OF BUOYAGE 
ON PACIFIC COAST. 

1. Red buoys with even numbers are placed on the star¬ 
board side of channels, and must be left on the starboard hand 
in passing inwards. 

2. Black buoys with odd numbers are placed on the port 
side of channels, and must be left on the port hand in pass¬ 
ing inwards. 

3. Buoys with red and black horizontal stripes are placed 
on obstructions, with channels on either side, and may be left 
on either hand in passing inwards. 

4. BuQys with white and black perpendicular stripes are 
placed in mid channel, and must be passed close to to avoid 
danger. 

5. Perches with balls, cages, etc., when placed on buoys, 
will be at turning points, the colors and numbers indicating on 
which side they should be passed. 

6. Different channels in the same bay, sound, river, or 
harbor, are usually marked by different kinds of buoys: prin¬ 
cipal channels by nun-buoys; secondary channels by can-buoys, 
and minor channels by spar buoys. Where there is but one 
channel, nun-buoys, properly colored and numbered, are in gen¬ 
eral use to mark the starboard side; and can-buoys, properly 
colored and numbered, to mark the port side. 

For fuller information, see “List of Beacons, Buoys and 
Day Marks of the Pacific Coast of the United States.” 





SUN'S DECLINATION 


93 


Sun’s Declination and Semi-Diameter for 1900 


JANUARY 


DATE 

DECLINATION 

HOURLY 

VARIATION 

semi-diameter 

17 

18 

28 

£9 

S. 20° 46' 31" .1 

20 34 32 .1 

l8 14 13 .1 

17 58 l6 .2 

29" -5 

30 .5 

39 -5 

40 -3 

W ft 

16 17 .0 

16 16 .9 

16 15 .8 

16 15 .7 

FEBRUARY 

26 

S. 8° 46' 26" . 1 

56" . 1 

16' 10" .4 

27 

8 23 56 .8 

56 -4 

16 10 .1 

MARCH 

8 

S. 4 0 56' 49" .6 

58 " .4 

16' 7".9 

9 

4 33 24 .8 

58 .6 

16 7 .7 

APRIL 

11 

N.. 8° 15' 11" .1 

55 " .1 

15 58" .7 

12 

8 37 10 .2 

54 -8 

15 58 .4 

JUNE 

3 

N. 22° 17' 44" .2 

18" .7 

15' 47 " *3 

4 

22 25 O .2 

17 .7 

15 47 -2 

5 

22 31 52 .7 

l6 .7 

15 47 -i 


JULY 


2 

N. 23 0 3 56" .8 

10 .9 

15' 45 " -3 

3 

22 59 24 .2 

11 .9 

15 45 -3 

4 

22 54 27 .6 

12 .9 

15 45 -3 

22 

20 19 55 -5 

29 .6 

15 46 .1 

23 

20 7 53 -7 

30 .5 

15 46 .2 

AUGUST 

6 

N. 16 0 46' 13" .1 

41" .1 

15 ' 47 ' -8 

7 

16 29 37 .8 

41 .8 

15 48 .O 

8 

16 12 46 .7 

42 .4 

15 48 .1 

17 

13 29 57 .5 

47 -8 

15 49 -6 

18 

13 10 43 .1 

48 -4 

15 49 .8 


SEPTEMBER 


14 

N. 3 0 29 39" -3 

57 " -6 

15' 55" -9 

15 

3 6 34 .8 

57 -7 

15 56 .2 

*9 

1 33 44 -3 

58 .2 

15 57 • 2 

20 

1 10 25 .3 

58 .3 

15 57 -5 


OCTOBER 


4 

S. 4 ° 

16' 

32" .6 

57 " 

•9 

16' 

1 

•4 

5 

4 

39 

41 .9 

57 

.8 

16 

1 

.6 

7 

5 

25 

49 -5 

57 

•5 

16 

2 

.2 

8 

5 

48 

47 -3 

57 

•3 

16 

2 

•3 

12 

7 

19 

50 .0 

56 

•4 

16 

3 

.6 

13 

7 

42 

21 .9 

56 

.2 

16 

*■> 

0 

9 


NOVEMBER 


5 

S. 15° 38' 

10" .7 

45 " -7 

r t " 

ID 9 .9 

6 1 

15 56 

20 .8 

45 - 1 

16 10 .1 

























































































NAUTICAL ALMANAC ELEMENTS FOR JANUARY, 1908 


SELF-INSTRUCTOR IN NAVIGATION 


Sidereal Time at 

Green. Mean Noon 

<N 00 O lOrJ-O^O H NN 

oo 4 4 t''. 4 O vo" w ov »o pi oo »o 

a 

n vo rr oo vo O o\ rorv m icov 

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A 

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Hourly 

Diff, 

C /1 

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MM M o O O00 N io in rj-rf fO 

tion of 
Add to 
Time 

cn 

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OvvO 0*0 Nm rf VO 0\m « (ON 

<tM M (ON VON MWfO 

3 • d 
p. 

a 

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h h o O On On to NvO fO w O 

Semi- 

Diameter 

t>» t^v£> vo vo vo low^ioioioio 

vOvOvOvOvOVOvOnOvOvOvOVOvOvO 

'u Itj 

0 -x 

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uovo 00 Ov m w O m r^oo OV Ov O m 

M M M M <N <N fO fO ro fO fO fO Tl-Tt 

+ 

PI Ov VO00 lOrtn OV M fOM N N« 

fOvO <OvO IO00 h 4 n<H 

Sun’s 

Declination 

ro m (S rj- M m m M rt iO*t N 

“t^M f>. Ov CO rf- O 00 PI t^M UOOvPO 
't'j-ci h lO'tCI lOfOfl rf <0 

ct 

W N « N N H O OW 00 00 00 NN 
NNNNNfKHNHHMMMM 

CO 

Hourly 

Diff. 

(0 

2 OvtOfOOVt^t^'-j-MCO UOMOO rj- 

O Ov ov ov00 00 VO vo <0 co <0 M (N 

Moooooooddoooo 

MMMMMMMMMMMMMM 

+ 

Sun’s Right 
Ascension 

CO 

Tj- rj- Ov t^CC vo coco CO o Ov O P0 

00 Pi O' m vovO O M O O OWO O’ O 

CN VO c 0 o- M CO M M n <0 4 

a 

t>» m o »0 <000 00 N PIVO o *tO 0 Pi 

uo M M « nif) CO CO rf rf ^ lo 

A 

00 ov ov Ov Ov Ov Ov o O O O O O O 

MMMMMMMP»ptC|p)p|P)P4 

Date 

O' «0 t>i 00 O M CO OvvO t^OO OV O M 
MMMMPIMMPICOCO 





















NAUTICAL ALMANAC ELEMENTS FOR FEBRUARY, 1902 


NAUTICAL ALMANAC ELEMENTS 


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+ 


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95 





































FROM NAUTICAL ALMANAC, APRIL, 1902 


96 


SELF-INSTRUCTOR IN NAVIGATION 


rt O 
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CO't't to to 

A 


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CO Tt- tOvO N- OV O M (N CO N 










































NAUTICAL ALMANAC ELEMENTS 


97 


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g-a 

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m co n- rt CN 
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O O O O O ON 

M_ M M M M 


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fa 

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NAUTICAL ALMANAC ELEMENTS FOR OCTOBER, 1902 


U8 


SELF-INSTRUCTOR IN NAVIGATION 


a 

m 

SIS 

- • 

Ck 


a o 
<v 

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H <5 

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w 

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MEAN PLACES OF STARS 


99 


FOR BEGINNING OF 1902. 


Mean Places of Stars Used in This Work. 


Name of 
Star 

Mag¬ 

nitude 

Right 

Ascension 

Annual 

Variat’n 

Declination 

Annual 

Variation 

Algenib .... 

3 

0 h 

08 m 

11.30s 

-4-3-085 

+ 14 0 

38 ’ 

19 - 5 ” 

+ 20.02” 

a. Arietis ... 

2 

2 

01 

38.80 

3-373 

+ 22 

59 

57-1 

17.14 

Polaris. 

2 

1 

23 

24.04 

25.628 

+88 

47 

04.1 

18.74 

\ldebaran. . 

1 

4 

30 

17.77 

3-439 

+ 16 

18 

45 0 

7.46 

Canopus ... 

1 

6 

21 

46.59 

1-332 

— 52 

38 

31-4 

— 1 89 

Sirius. 

1 

6 

40 

4978 

2.644 

— 16 

34 

53-6 

476 

Castor. 

2 

7 

28 

20.89 

3835 

+ 32 

06 

13-9 

7.62 

Procyon.... 

1 

7 

34 

10.34 

3-143 

+ 5 

28 

345 

9.04 

Spica. 

1 

13 

20 

01.74 

3-155 

— 10 

38 

59-3 

18. S7 

Arcturus ... 

1 

14 

11 

11.47 

2-735 

+ 19 

4 i 

33-0 

18.85 

Antares .... 

1 

16 

23 

23.82 

3.672 

— 26 

12 

52.9 

8.23 

Altair. 

1 

19 

46 

00.12 

2.927 

+ 8 

36 

33-3 

+ 9-32 

Fomalhaut.. 

i -5 

22 

52 

14.22 

3-324 

— 30 

08 

30.2 

19.00 


ANSWERS. 


MULTIPLICATION BY LOGARITHMS 

I. 729.6, 2. 1201200, 3. 2027, 4, .OI44445. 

DIVISION BY LOGARITHMS 

I. 47, 2. 49.97, 3- 43 26 4°. 4- .0161. 

PARALLEL SAILING 

I. 59 97, 2. 65.92. 3. 5I.7, 4. 419.96. 

DAYS WORK 

1. True Courses —N. 2 pts. W. 6 miles; N. 1 W. 17 m; N. 

W. 18; S. 4 W. 22; S. 5}4 w. 25; S. 5 W. 26; S. 23^ E. 28; N. 4 
W. 28. 

Diff. Lat. 7'.3 S. Dep. 76+ W.; Lat. in 3S 0 9 N.; Diff. Long 
97 miles. 





























100 SELF-INSTRUCTOR IN NAVIGATION 


Long, in 13 0 37' E.; Course S. 85° W.; distance 77 miles. 

2. True Courses —S. 89° W. 5; N. 23 0 W. 29; N. 37 0 W. 31; 
N. 46° W. 33; N. 36° W. 32; S. 41 0 W. 30.; S. 67° W. 29; N. 29° 
W. 30. 

Diff. Lat. 92'.5 N.; Dep. i38'.4 W.; Lat. in 41 0 53' N.; Diff. 
Long. 184 miles. 

Long, in 128° 24 W.; course N. 56° W.; distance 167 miles. 

3. True Courses —S. 7 pts. E. 12 m.; N. 4E. 25; N. 2E. 26; 
N. 1 E. 33; S. zVa K. 30; S. 1 E. 26; S. 7 yi W. 22; N. 2 E. 24. 

Diff. Lat. 43.0 N.; Dep. 60.7 E.; Lat. in 49 0 46' S.; Diff. Long. 
94 miles. 

Long, in 57 0 46' W.; course N. 55 0 E.; distance 74 miles. 

LATITUDE BY SUN’S MERIDIAN ALTITUDE 

t. A. T. Green. 26 d 13 h 57 mo s; Corr. Decl. 8° 33' 21" S.; 
True Alt. 50° 15' 35"; Latitude, 48° 17' 46" South. 

2. A. T. Green. 17 d 8 h 30 m 40 s; Decl. 20° 42' 20" S.; True 
Alt. 56° n' 50"; Latitude, 6o° 30' 24" South. 

3. A. T. Green. 6 d 21 h 36 m; Decl. 16 0 31' 18" N.; T. Alt. 
62° 45' 48"; Latitude 43 0 45' 30" North. 

4. A. T. Green. 4 d 11 h 55 m 20 s; Decl. 22° 28' 31" N.; T. 
Alt. 69° 29' 50"; Latitude, i° 58' 21" North. 

5. A. T. Green. 12 d 16 h 20 m 4 s; Decl. 7 0 35' 9" S.; T. Alt. 
6i° 18' 24"; Latitude, 21 0 06' 27" North. 

mercator’s sailing 

1. Diff Lat. 734; Mer. diff. Lat. 1004; Diff. long. 264; Course 
S. 14 0 44 E.; Dist. 758.9 miles. 

2. Diff. Lat. 1392; Mer. diff Lat. 1403; Diff. long. 1712; Course 
S. 50° 40' E.; Dist. 2196 miles. 

3. Diff. Lat. 1325; Mer. diff. Lat. 1334; Diff. long. 4358; Course 
S. 72 0 59'E.; Dist. 4528 miles. 

4. Diff. Lat. 607; Mer. diff. Lat. 909; Diff. long. 3793; Course 
N. 76° 31^' W.; Dist. 2605 miles. 

amplitudes 

1. Err. 5 0 55' 30" W.; Dev. 4 0 04' 30" E. 

2. Err. io° 29' 30" W.; Dev. 20° 34 30" W. 

3. Err. 16 0 15' 30" E.; Dev. 4 0 15' 30" E. 


ANSWERS 


101 


4. A. T. G. 22 d 19I1 35 m 54 s; Decl. 20° 10' 14" N.; T. Amp. 
W. 32 0 3' N.; Err. 8° 33' E.; Dev. 3 0 27' W. 

5. A. T. G. 5 d 23 h 18 m 50 s; Decl. 15 0 55' 49" S.; T. Amp. 
W. 22 0 13 30" S.; Err. 5 0 21' W.; Dev. 3 0 9' E. 

LONGITUDE BY CHRONOMETER 

1. M. T. G. 16 d 19 h 16 m 45 s; Decl. 23 0 19' 56" S.; Equ. 
Time,—4 m 13 s ; True Alt. 27 0 13' 08"; Hour Angle 3 h 24 m 
42 s; Long. 120° 56' East. 

2. M. T. G. 4 d 7 h 40 m 19 s; Decl. 22 0 23' 44" N.; Equ. 
Time,—2 mis; True Alt. 41 0 12' 23"; H. Angle 3 h 23 m 29 s; 
Long. 166° 27' 15" West. 

3. M. T. G. 9 d 19 h 2 m 3 s; Decl. 22 0 50' 33" S.; Equ. Time, 
—7 m 30 s; True Alt. 12 0 39' 42"; H. Angle 3 h 56 m 19 s; Long, 
at Sights 131 0 41' 30" East; Long, at Noon 132 0 07' 30" East. 

4. M. T. G. 11 h 7 h 07 m 37 s; Daily Rate 3.7 s; Decl. 17 0 
47' 04" N.; Equ. Time,—3 m 45 s; True Alt. io° 33' 41"; H. Ang. 
3 h 54 m 37 s; Long. 166 0 29' 45" West. 

ALTITUDE AZIMUTHS 

1. True Azim. N. 51 0 54 W.; Error 9 0 43' W.; Deviation 6° 
17' East. 

2. True Azim. N. 46° 02' E.; Error 12 0 17' E.; Deviation 4 0 
54 West. 

3. True Azim. S. 84°* 51' W.; Error 8° 29' W.; Deviation 22 0 
34 West. 

4. True Azim. S. 86° 2' E.; Error 9 0 36' E.; Deviation n° 40' 
East. 

TIME AZIMUTHS 

1. True Azim. S. io3°4 W. 2. True Azim. N. 109° 34 E. 
3. True Azim. N. 135 0 4 E. 4. True Azim. S. 134 0 19' W. 

REDUCTIONS 

1. A. T. G. Jan. 4dnh4mis; Decl. 22 0 44 45" S*; True 
Alt. 33 0 8' 51"; Time From Noon 26 m 25 s; Natural Number 
510; Latitude, 33 0 45' North. 

2. A. T. G. 15 d 19 h 32 m 26 s; Decl. 21 0 31' 12" N.; True 
Alt. 42 0 49' 59"; Time From Noon 13 m 54 s; Number 155; Lat. 
25 0 31' 48" South. 

3. A. T. G. 6 d 9 h 50 m 42 s; Decl. 22 0 43' 45" N.; True Alt. 


102 


SELF-INSTRUCTOR IN NAVIGATION 


28° 9 ; Time From Noon 23 m 46 s; Number 387.1; Latitude 38^ 
52' 15* South. 

4. M. T. G. 9 d 6 h 5 m 51 s; Decl 15 0 59' 26" N.; Equ. Time, 
—5 m 25 s; True Alt. 43 0 51' 58"; Time From Noon 21 m 58 s; 
Number 384.0; Latitude, 29 0 50' 13" South. 

STAR LATITUDE 

1. True Alt. 53 0 53'40"; Decl. 14 0 38' 19" N.; Latitude 50° 
44' 39" North. 

2. True Alt. 52 0 41' 16"; Decl. 26° 12' 53" S.; Latitude 63° 31' 
37" South. 

3. True Alt. 64° 13' 25"; Decl! 32 0 6' 14" N.; Latitude 6° 19 
39" North. 

4. True Alt. 55 0 56' 15"; Decl. 16 0 18' 45" N.; Latitude 50° 22' 
30" North. 

POLARIS 

1. M. T. G. 12 d 18 h 32 m 38 s; Sid. Time at Obs. 14 h 20 rr 
49 s; Red. Alt. 41 0 4 09"; Latitude 42 0 14 12" North. 

2. M. T. G. 21 d 4 h 2 m 4 s; Sid. Time at Obs. 2 h 8 m 21 s- 
Red. Alt. 29 0 55' 18"; Latitude 28° 44 18" North. 

STAR LONGITUDE 

1. M. T. G. 8 d 2 h ii m 15 s; T. Alt. 41 0 54 39"; P. D. 59° 

51' 30*; Red. Sid. T. 9 h 4 m 36 s; H. Ang. W. 3 h 57 m 31 s; R. 

A. Mer. 2 h 49 m 45 s; M. T. S. 7 d 17 h 45 m 9 s; Longitude 
126° 31' 30" West. 

2. M. T. G. 28 d 21 h 26 m 45 s; T. Alt. 22 0 14 20"; P. D. 

106 0 34 54"; Red. Sid. T. 20 h 30 m 47 s; H. Ang. E. 1 h 1 m 

38 s; R. A. Mer. 5 h 39 m 12 s; M. T. S. 29 d 9 h 8 m 25 s; 

Longitude 175 0 25' 00" East. 

SUMNER 

1. Line of Bearing at tkne of first Obs. N. 56° E. Suns True 
Bearing S. 34 0 E. Ship’s pos. at time of second Obs. Lat. 50° 
27' N.; Long. 9 0 23' W. 

2. Line of Bearing at time of first Obs. N. 64° W.; Sun’s True 
Bearing S. 26° W.; Ship’s pos. at time of second Obs. Latitude 
49 0 43' N.; Long. 170° 28' W. 

Johnson’s method 

1. Corr. for second Lat. 3.1'; Corr. for Long. 1 5.2'; Corr. for 


THE BEAUFORT NOTATION 103 

Long. 2 13.2'; Latitude 46° 46' 18" N.; Longitude 163° 20' 33" E. 

STAR AZIMUTH 

1. a. T. G. 19 d 9 h 34 m 16 s; Red. Sun’s R. A. 13I1 34 m 
42 s; R. A. Mer. 5 h 36 m 42 s; Hour Ang. E. 1 h 4 m 8 s; True 
Azim. N. 24 0 E.; Comp. Err. 27 0 40' E.; Deviation 17 0 50' East. 

2. M. T. S. 18 d 8 h 30 m 10 s; Red. Sid. Time 19 h 49 m o s; 
R. A. Mer. 4 h 19 m 10 s; H. Ang. W. 2 h 17 m 31 s; T. Azim. 
N. 33 0 30' W.; Comp. Err. 2 0 o' E. Deviation n° 10' West. 


THE BEAUFORT NOTATION. 


INDICATING THE FORCE OF THE WIND 


0. 

Denotes calm. 

6 . 

Strong breeze. 

I. 

Light air: just sufficient 

7 - 

Moderate gale. 

> give steerage way. 

8 . 

Fresh gale. 

2. 

Light breeze. 

9 - 

Strong gale. 

3 - 

Gentle breeze. 

10. 

Whole gale. 

4 * 

Moderate breeze. 

11. 

Storm. 

5 - 

Fresh breeze. 

12. 

Hurricane 


INDICATING THE WEATHER 

b. 

Blue sky. 

P- 

Passing showers. 

c. 

Clouds (detached.) 

q- 

Squally. 

d. 

Drizzling rain 

r. 

Rain. 

f. 

Foggy. 

s. 

Snow. 

g- 

Gloomy. 

t. 

Thunder. 

h. 

Hail. 

u. 

Ugly (threatening). 

1. 

m. 

Lightning. 

Misty. 

V. 

tt- \ remarkable vis. 

Visibility 1 Q f distant objects 

0. 

Overcast. 

w. 

Wet (dew). 


A bar (—) under any letter augments its signification; thusj^ 
very foggy; heavy rain, etc. 

Note :—The above has been added owing to the request of brothei 
Navigators. 




PILOT RULES 


- FOR - 

ATLANTIC AND PACIFIC COAST INLAND WATEES. 


Buies and Regulations for the government of 'pilots of vessels 
propelled by steam, gas, fluid, naphtha, or electric motors, 
or of other vessels propelled by machinery, navigating the 
harbors, rivers, and inland waters of the United States 
(except the Great Lakes and their connecting and tribu¬ 
tary waters as far east as Montreal, the Red River of the 
North, and rivers emptying into the Gulf of Mexico, and 
their tributaries). Adopted by the Board of Supervising 
Inspectors of Steam Vessels January 26 , 1899 , under the 
authority of an act of Congress approved June 7, 1897 . 

In the following rules the words “steam vessel” and “steamer” 
shall include any vessel propelled by machinery. 


EEGULATIONS FOE PEEVENTING COLLISIONS 
AT SEA. 

PRELIMINARY. 

In the following rules every steam vessel which is under 
sail and not under steam is to be considered-a sailing vessel, and 
every vessel under steam, whether under sail or not, is to be 
considered a steam vessel. 

The word “steam-vessel” shall include any vessel propelled 
by machinery. 

A vessel is “under way,” within the meaning of these 
rules, when she is not at anchor, or made fast to the shore, or 
aground. 

RULES CONCERNING LIGHTS, ETC. 

L The word “visible” in these rules, when applied to lights, 




RULES OF THE ROAD 


105 


shall mean visible on a dark night with a clear atmosphere. 

Article 1 . The rules concerning lights shall be com¬ 
plied with in all weathers from sunset to sunrise, and during 
such time no other lights which may be mistaken for the pre¬ 
scribed lights shall be exhibited. 

Art. 2. A steam vessel when under way shall carry: 

(a) On or in front of the foremast, or, if a vessel with¬ 
out a foremast, then in the fore part of the vessel, a bright 
white light so constructed as to show an unbroken light over 
an arc of the horizon of twenty points of the compass, so fixed 
as to throw the light ten points on each side of the vessel, 
namely, from right ahead to two points abaft the beam on either 
side, and of such a character as to be visible at a distance of at 
least five miles. 

(b) On the starboard side a green light so constructed as 
to show an unbroken light over an arc of the horizon of ten 
points of the compass, so fixed as to throw the light from right 
ahead to two points abaft the beam on the starboard side, and 
of such a character as to be visible at a distance of at least 
two miles. 

(c) On the port side a red light so constructed as to show 
an unbroken light over an arc of the horizon of ten points of 
the compass, so fixed as to throw the light from right ahead to 
two points abaft the beam on the port side, and of such a char¬ 
acter as to be visible at a distance of at least two miles. 

(d) The said green and red side-lights shall be fitted 
with inboard screens projecting at least three feet forward from 
the light so as to prevent these lights from being seen across 
the bow. 

(e) A sea-going steam vessel when under way may carry 
an additional white light similar in construction to the light 
mentioned in subdivision (a). These two lights shall be so 
placed in line with the keel that one shall be at least fifteen feet 
higher than the other, and in such a position with reference to 
each other that the lower light shall be forward of the upper 
one. The vertical distance between these lights shall be less 
■ban the horizontal distance. 


106 SELF-INSTRUCTOR IN NAVIGATION 


Art. 3 . A steam-vessel when towing another vessel, shall, 
in addition to her side lights, carry two bright white lights in 
a vertical line one over the other, not less than three feet apart, 
and when towing more than one vessel shall carry an additional 
bright white light three feet above or below such lights, if the 
length of the tow, measuring from the stern of the towing ves¬ 
sel to the stem of the last vessel towed, exceeds six hundred 
feet. Each of these lights shall be of the same construction 
and character, and shall be carried in the same position as 
the white light mentioned in article two (a). 

Such steam vessel may carry a small white light abaft the 
funnel or aftermast for the vessel towed to steer by, but such 
light shall not be visible forward of the beam. 

Art 5 . A sailing vessel under way or being towed shall 
carry the same lights as are prescribed by article two for a 
steam-vessel under way, with the exception of the white lights 
mentioned therein, which they shall never carry. 

Art. 6. Whenever, as in the case of vessels of less than 
ten gross tons under way during bad weather, the green and 
red side-lights can not be fixed, these lights shall be kept at 
hand, lighted and ready for use; and shall, on the approach 
of or to other vessels, be exhibited on their respective sides in 
sufficient time to prevent collision, in such manner as to make 
them most visible, and so that the green light shall not be seen 
on the port side, nor the red light on the starboard side, nor, 
if practicable, more than two points abaft the beam on their 
respective sides. To make the use of these portable lights 
more certain and easy the lanterns containing them shall each 
be painted outside with the color of the light they respectively 
contain, and shall be provided with proper screens. 

Art. 7 . Rowing boats, whether under oars or sail, shall 
have ready at hand a lantern showing a white light which shall 
be temporarily exhibited in sufficient time to prevent collision. 

Art. 8. Pilot vessels when engaged on their station on 
pilotage duty shall not show the lights required for other vessels, 
but shall carry a white light at the masthead, visible all around 
the horizon, and shall also exhibit a flare-up light or flare-up 


RULE OF THE ROAD 


107 


lights at short intervals, which shall never exceed fifteen 
minutes. 

On the near approach of or to other vessels they shall have 
their side lights lighted, ready for use, and shall flash or show 
them at short intervals, to indicate the direction in which they 
are heading, but the green light shall not be shown on the port 
side nor the red light on the starboard side. 

A pilot-vessel of such a class as to be obliged to go along¬ 
side of a vessel to put a pilot on board may show the white light 
instead of carrying it at the masthead, and may, instead of the 
colored lights above mentioned, have at hand, ready for use, a 
lantern with a green glass on the one side and a red glass on the 
other, to be used as prescribed above. 

Pilot-vessels, when not engaged on their station on pilot¬ 
age duty, shall carry lights similar to those of other vessels ot 
their tonnage. 

Art. 9 . (a) Fishing vessels of less than ten gross tons, 

when under way and when not having their nets, trawls, 
dredges, or lines in the water, shall not be obliged to carry the 
colored side lights; but every such vessel shall, in lieu thereof, 
have ready at hand a lantern with a green glass on one side and 
a red glass on the other side, and on approaching to or being 
approached by another vessel such lantern shall be exhibited 
in sufficient time to prevent collision, so that the green light 
shall not be seen on the port side nor the red light on the 
starboard side. 

(b) All fishing vessels and fishing boats of ten gross tons 
or upward, when under way and when not having their nets, 
trawls, dredges, or lines in the water, shall carry and show the 
same lights as other vessels under ^vay. 

(c) All vessels, when trawling, dredging, or fishing with 
any kind of drag-nets or lines, shall exhibit, from some part of 
the vessel where they can be best seen, two lights. One of these 
lights shall be red and the other shall be white. The red light 
shall be above the white light, and shall be at a vertical distance 
from it of not less than six feet and not more than twelve feet; 
and the horizontal distance between them, if any, shall not be 


108 SELF-INSTRUCTOR IN NAVIGATION 

more than ten feet. These two lights shall he of such a char¬ 
acter and contained in lanterns of such construction as to be 
visible all around the horizon, the white light a distance of not 
less than three miles and the red light of not less than two miles. 

Art. 10. A vessel which is being overtaken by another, 
except a steam-vessel with an after range-light showing all 
around the horizon, shall show from her stern to such last- 
mentioned vessel a white light or a flare-up light. 

Art. 11. A vessel under one hundred and fifty feet in 
length when at anchor shall carry forward, where it can best 
be seen, but at a height not exceeding twenty feet above the hull, 
a white light, in a lantern so constructed as to show a clear, 
uniform, and unbroken light visible all around the horizon at a 
distance of at least one mile. 

A vessel of one hundred and fifty feet or upwards in length 
when at anchor shall carry in the forward part of the vessel, at a 
height of not less than twenty and not exceeding forty feet 
above the hull, one such light, and at or near the stem of the 
vessel, and at such a height that it shall be not less than fifteen 
feet lower than the forward light, another such light. 

The length of a vessel shall be deemed to be the length ap¬ 
pearing in her certificate of registry. 

Art. 12. Every vessel may, if necessary, in order to at¬ 
tract attention, in addition to the lights which she is by these 
rules required to carry, show a flare-up light or use any deton¬ 
ating signal that can not be mistaken for a distress signal. 

Art. 13 . Nothing in these rules shall interfere with the 
operation of any special rules made by the government of any 
nation with respect to additional station and signal lights for 
two or more ships of war or for vessels sailing under convoy, or 
with the exhibition of recognition signals adopted by ship¬ 
owners, which have been authorized by their respective govern¬ 
ments, and duly registered and published. 

Art. 14 . A steam-vessel proceeding under sail only, but 
having her funnel up, may carry in daytime, forward, where 
it can best be seen, one black ball or shape two feet in diameter. 


RULE OF THE ROAD 


109 


SOUND SIGNALS FOR FOG, ETC. 

Art. 15 . All signals prescribed by this article for vessels 
under way shall be given : 

1 . By “steam-vessels” on the whistle or siren. 

2 . By “sailing-vessels’’ and “vessels towed” on the fog 

horn. 

The words “prolonged blast” used in this article shall 
mean a blast of from four to six seconds duration. 

A steam vessel shall be provided with an efficient whistle 
or siren, sounded by steam or by some substitute for steam, so 
placed that the sound may not be intercepted by any obstruc¬ 
tion, and with an efficient fog horn; also with an efficient bell. 
A sailing vessel of twenty tons gross tonnage or upward shall 
be provided with a similar fog horn and bell. 

In fog, mist, falling snow, or heavy rainstorms, whether 
by day or night, the signals described in this article shall be 
used as follows, namely: 

(a) A steam-vessel under way shall sound, at intervals 
of not more than one minute, a prolonged blast. 

(c) A sailing vessel under way shall sound, at intervals 
of not more than one minute, when on the starboard tack, one 
blast; when on the port tack, two blasts in succession, and when 
with the wind abaft the beam, three blasts in succession. 

(d) A vessel when at anchor shall, at intervals of not 
more than one minute, ring the bell rapidly for about five 
seconds. 

(e) A steam-vessel when towing, shall, instead of the 
signals prescribed in subdivision (a) of this article, at intervals 
of not more than one minute, sound three blasts in succession, 
namely, one prolonged blast followed by two short blasts. A 
vessel towed may give this signal and she shall not give any 
other. 

SPEED OF SHIPS TO BE MODERATE IN FOG, ETC. 

Art. 16 . Every vessel shall, in a fog, mist, or falling 
mow, or heavy rainstorms, go at a moderate speed, having care¬ 
ful regard to the existing circumstances and conditions. 


no 


SELF-INSTRUCTOR IN NAVIGATION 


A steam-vessel hearing, apparently forward of her beam, 
the fog signal of a vessel the position of which is not ascertained 
shall, so far as the circumstances of the case admit, stop her 
engines, and then navigate with caution until danger of collision 
is over. 

STEERING AND SAILING RULES—PRELIMINARY— 

RISK OF COLLISION. 

Risk of collision can, when circumstances permit, be ascer¬ 
tained by carefully watching the compass bearing of an ap¬ 
proaching vessel. If the bearing does not appreciably change, 
such risk should be deemed to exist. 

Art. 17 . When two sailing vessels are approaching one 
another, so as to involve risk of collision, one of them shall keep 
out of the way of the other as follows, namely: 

(a) A vessel which is running free shall keep out of the 
way of a vessel which is close-hauled. 

(b) A vessel which is close-hauled on the port tack 
shall keep out of the way of a vessel which is close-hauled on the 
starboard tack. 

(c) When both are running free, with the wind on dif¬ 
ferent sides, the vessel which has the wind on the port side shall 
keep out of the way of the other. 

(d) When both are running free, with the wind on the 
?ame side, the vessel which is to the windward shall keep out of 
the way of the vessel which is to the leeward. 

(e) A vessel which has the wind aft shall keep out of the 
way of the other vessel. 

Art. 18 . Rule 1. When steam-vessels are appioaching 
each other head and head, that is, end on, or nearly so, it shall 
be the duty of each to pass on the port side of the other; and 
either vessel shall give, as a signal of her intention, one short 
and distinct blast of her whistle, which the other vessel shall 
answer promptly by a similar blast of her whistle, and there¬ 
upon such vessels shall pass on the port side of each other. But 
if the courses of such vessels are so far on the starboard of each 
other as not to be considered as meeting head and head, either 


RULE OF THE ROAD 


111 


vessel shall immediately give two short and distinct blasts 
of her whistle, which the other vessel shall answer prompt¬ 
ly by two similiar blasts of her whistle, and they shall pass 
on the starboard side of each other. 

The foregoing only applies to cases where vessels are 
meeting end on or nearly end on, in such a manner as to 
involve risk of collision; in other words, to cases in which, 
by day, each vessel sees the masts of the other in a line, 
or nearly in a line, with her own, and by night to cases in 
which each vessel is in such a position as to see both the 
side-lights of the other. 

It does not apply by day to cases in which a vessel 
sees another ahead crossing her own course, or by night to 
cases where the red light of one vessel is opposed to the 
red light of the other, or where the green light of one ves¬ 
sel is opposed to the green light of the other, or where a 
red light without a green light or a green light without a 
red light, is seen ahead, or where both green and red lights 
are seen anywhere but ahead. 

Rule II. When steamers are approaching each other 
in an oblique direction, so as to involve risk of collision, 
the vessel which has the other on her own starboard side 
shall keep out of the way of the other, which latter vessel 
shall keep her course and speed; the steam-vessel having 
the other on her starboard side indicating by one blast 
of her whistle her intention to direct her course to star¬ 
board, so as to cross the stem of the other steamer; and 
two blasts her intention of directing her course to port, 
which signals must be promptly answered by the steamer 
having the right of way, but the giving and answering 
signals by a vessel required to keep her course shall not 
vary the duties and obligations of the respective vessels. 

Rule III. If, when steam-vessels are approaching 
each other, either vessel fails to understand the course or 
intention of the other, from any cause, the vessel so in 
doubt shall immediately signify the same by giving several 
short and rapid blasts, not less than four, of the steam 
whistle. 

Rule IV When steamers are running in a fo°\ mist, falling 
snow, or heavy rainstorms, except when towing, it shall be 


112 


SELF-INSTRUCTOR IN NAVIGATION 


the duty of the pilot to cause a long blast of the whistle to be 
sounded at intervals not exceeding one minute. 

A steam-vessel w T hen towing shall, at intervals of not more 
than one minute, sound three blasts in succession, namely, one 
prolonged blast, followed by two short blasts. A vessel towed 
may give this signal, and she shall not give any other. 

A vessel is “under way” within the meaning of these rules, 
when she is not at anchor, or made fast to the shore, or aground. 

Every steam-vessel shall, in a fog, mist, falling snow, or 
heavy rainstorms, go at a moderate speed, having careful regard 
to the existing circumstances and conditions. 

A steam-vessel hearing, apparently forward of her beam, 
the fog signal of a vessel the position of which is not ascer¬ 
tained shall, so far as the circumstances of the case admit, stop 
her engines, and then navigate with, caution until danger of 
collision is over. 

Rule V. Whenever a steam-vessel is nearing a short bend 
or curve in the channel, where, from the height of the banks or 
other cause, a steam-vessel approaching from the opposite direc¬ 
tion can not be seen for a distance of half a mile, such steam- 
vessel, when she shall have arrived within half a mile of such 
curve or bend, shall give a signal by one long blast of the steam 
whistle, which signal shall be answered by a similar blast, given 
by any approaching steam-vessel that may be Avithin hearing. 
Should such signal be so answered by a steam-vessel upon the 
farther side of such bend, then the usual signals for meeting 
and passing shall immediately be given and answered; but, if 
the first alarm signal of such vessel be not answered, she is to 
consider the channel clear and govern herself accordingly. 

When steam-vessels are moved from their docks or berths, 
and other boats are liable to pass from any direction toward 
them, they shall give the same signal as in the ease of vessels 
meeting at a bend, but immediately after clearing the berths so 
as to be fully in sight they shall be governed by the steering and 
sailing rules. 

Rule VIII. When steam-vessels are running in the same 
direction, and the vessel which is astern shall desire to pass on 


RULE OF THE ROAD 


113 

the right or starboard hand of the vessel ahead, she shall give 
one short blast of the steam whistle, as a signal of such desire, 
and if the vessel ahead answers with one blast, she shall put her 
helm to port; or if she shall desire to pass on the left or port 
side of the vessel ahead, she shall give two short blasts of the 
steam whistle as a signal of such desire, and if the vessel ahead 
answers with two blasts, shall put her helm to starboard; or 
if the vessel ahead does not think it safe for the vessel astern to 
attempt to pass at that point, she shall immediately signify the 
same by giving several short and rapid blasts of the steam 
whistle, not less than four, and under no circumstances shall the 
vessel astern attempt to pass the vessel ahead until such time 
as they have reached a point where it can be safely done, when 
said vessel ahead shall signify her willingness by blowing the 
proper signals. The vessel ahead shall in no case attempt to 
cross the bow or crowd upon the course of the passing vessel. 

Rule IX. The whistle signals provided in the rules under 
this article, for steam-vessels meeting, passing, or overtaking, 
are never to be used except when steamers are in sight of each 
other, and the course and position of each can be determined in 
the daytime by a sight of the vessel itself, or by night by seeing 
its signal lights. In fog, mist, falling snow, or heavy rain¬ 
storms, when vessels can not so see each other, fog signals only 
must be given. 

Art. 19 . When two steam-vessels are crossing, so as to 
involve risk of collision, the vessel which has the other on h<?r 
own starboard side shall keep out of the way of the otiior. 

Art. 20. When a steam-vessel and a sailing vessel are 
proceeding in such directions as to involve risk of collision, the 
steam-vessel shall keep out of the way of the sailing vessel. 

Art. 21 . Where, by any of these rules, one of the two 
vessels is to keep out of the wav, the other shall keep her course 
and speed. 

Art. 22 . Every vessel which is directed by these rules to 
keep out of the way of another vessel shall, if the circumstances 
of the case admit, avoid crossing ahead of the other. 

Art. 23 . Every steam-vessel which is directed by these 


114 SELF INSTRUCTOR IN NAVIGATION 


rules to keep out of the way of another vessel shal], on ap¬ 
proaching her, if necessary, slacken her speed or stop or 
reverse. 

Art. 24 . Notwithstanding anything contained in 
these rules every vessel, overtaking any other, shall keep 
out of the way of the overtaken vessel. 

Every vessel coming up with another vessel from any 
direction more than two. points abaft her beam, that is, 
in such a position with reference to the vessel which she is 
overtaking that at night she would be unable to see either 
of that vessel’s side lights, shall be deemed to be an over¬ 
taking vessel; and no subsequent alteration of the bearing 
between the two vessels shall make the overtaking vessel 
a crossing vessel within the meaning of these rules, or re¬ 
lieve her of the duty of keeping clear of the overtaking 
vessel until she is finally past and clear. 

As by day the overtaking vessel can not always know 
with certainty whether she is forward of or abaft this di¬ 
rection from the other vessel she should, if in doubt, as¬ 
sume that she is an overtaking vessel and keep out of the 
way. 

Art. 25 . In narrow channels every steam-vessel shall, 
when it is safe and practicable, keep to that side of the 
fairway or mid-channel which lies on the starboard side 
of such vessel. 

Art. 26 . Sailing vessels under way shall keep out of 
the way of sailing vessels or boats fishing with nets, or 
lines, or trawls. This rule shall not give to any vessel 
or boat engaged in fishing the right of obstructing a fair¬ 
way used by vessels other than fishing vessels or boats. 

Art. 27 . In obeying and construing these rules due 
regard shall be had to all dangers of navigation and colli¬ 
sion, and to any special circumstances which may render 
a departure from the above rules necessary in order to 
avoid immediate danger. 

SOUND SIGNALS FOR VESSELS IN SIGHT OF ONE 
ANOTHER, 

Art. 28 . When vessels are in sight of one another a steam 
vessel under way whose engines are going at full speed 


RULE OF THE ROAD 


115 


astern shall indicate that fact by three short blasts on the 
whistle. 

NO VESSEL UNDER ANY CIRCUMSTANCES TO NEGLECT 
PROPER PRECAUTIONS. 

Art. 29. Nothing in these rules shall exonerate any ves¬ 
sel, or the owner or master or crew thereof, from the conse¬ 
quences of any neglect to carry lights or signals, or of any neg¬ 
lect to keep a proper lookout, or of the neglect of any precaution 
which may be required by the ordinary practice of seamen, or 
by the special circumstances of the case. 

Art. 30. The exhibition of any light on board of a vessel 
of war of the United States or a revenue cutter may be sus¬ 
pended whenever, in the opinion of the Secretary of the Navy, 
the commander in chief of a squadron, or the commander of a 
vessel acting singly, the special character of the service may 
require it. 


AIDS TO MEMORY IN VERSE 


By Thomas Gray. 


1. Two Steamships Meeting: 

When both side lights I see ahead, 

I port my helm and show my red . 

2. Two Steamships Passing: 

Green to green, or red to red — 

Perfect safety—go ahead! 

3. Two Steamships Crossing: 

Note .—This is the position of greatest danger; there is 
nothing for it but good lookout, caution and judgment. 

If to my starboard red appear, 
it is my duty to keep clear; 






116 


SELF-INSTRUCTOR IN NAVIGATION 


To act as judgment says is proper— 

To port, or starboard, back, or stop her! 

But when upon my port is seen 
A steamer’s starboard light of green. 

For me there’s nought to do but see 
That green to port keeps clear of me. 

4. All Ships Must Keep a Good Lookout, and Steam¬ 
ships Must Stop and Go Astern f if Necessary. 

Both in safety and in doubt 
I always keep a good lookout; 

In danger, with no room to turn, 

I ease her! Stop her! Go astern! 


DISTRESS SIGNALS. 

Art. 31. When a vessel is in distress and requires the 
assistance from other vessels or from the shore the following 
shall be the signals to be used or displayed by her, either to¬ 
gether or separately, namely: 

IN THE DAYTIME. 

A continuous sounding with any fog signal apparatus, or 
firing a gun. 

AT NIGHT. 

First. Flames on the vessel as from a burning tar barrel, 
oil barrel, and so forth. 

Second. A continuous sounding with any fog signal ap¬ 
paratus, or firing a gun. 



LATITUDE BY MERIDIAN ALTITUDE OF 
THE MOON. 


Usually, when conditions are favorable for observing 
altitudes of the moon to obtain ship’s position at sea, star ob 
servations can be bad to better advantage, giving better re¬ 
sults. Because of this fact, the former has not thus far been 
given space in the Self-Instructor, although the writer has 
often felt much obliged to the moon for the light she has 
thrown on the horizon while he has been observing stars. 

To comply, however, with the desire of some patrons of 
the work, this second issue contains, with other additions, 
latitude by meridian altitude of the moon; for occasions do 
arise at sea, when the longed-for latitude can be determined by 
a snap shot of “Fair Luna.” 

RULES. 

1. Take out from page 4 for the month in the Nautical 
Almanac, the moon’s upper meridian passage, or upper transit, 
for the astronomical day at the head of the question. This 
will mean the day before, if A. M., or same day, if P. M. Take 
this element out also for the day before, if east longitude, or 
day after, if in west longitude. 

NOTE.—If the Nautical Almanac gives no meridian pas¬ 
sage, or transit, the sun will then be in conjunction with the 
moon. 

2. Subtract the least meridian passage from the greatest 
and call the remainder retardation. Multiply this by the 
longitude in time and divide by 24 and we have the correction 
for the meridian passage of the astronomical day, to be added, 
if the longitude is west, or subtracted if the longitude is east. 
The result is the ship mean time of meridian passage, and 
must be dated for the previous day, if A. M„ or same day, if 
P. M. question. To the ship mean time of meridian passage 
add the longitude in time, if west, or subtract, if east, and w* 
have mean time at Greenwich. 



318 


SELF-INSTRUCTOR IN NAVIGATION 


3. Now correct the moon’s declination, semi-diameter 
and horizontal parallax, as follows. 

THE DECLINATION. 

4. From Nautical Almanac, pages 5 to 12, for the month 
take out the declination for the day and hour of mean time at 
Greenwich, also the difference for 1 minute; multiply this 
difference by the minutes and tenths of a minute in the 
Greenwich time, and we have the correction for the declina 
tion, to be added if increasing, or subtracted if decreasing. 

Example: 

Example, 1902, Feb. 25th. .9I1 01m 30s M. T. G. ; what is the moon’s 
declination?. 1. 5 

Supposed decl. on 25d 9h=7° 57’ 08” .9 S Diff. in 1 min. 

Decl. incr. —- Corr. -j- 14. 4 9”.582 

Corr. decl. 7 .57 .23 .“3 S _ 1.5 

479io 

14.3730 

NOTE.—The approximate latitude used for correcting the 
horizontal parallax is found by subtracting the altitude from 
90°, and applying the declination to nearest degree. 

SEMI-DIAMETER AND HORIZONTAL PARALLAX. 

5. From Nautical Almanac, page 4 of the month, take 
out the semi-diameter and horizontal parallax for both noon 
and midnight of the Greenwich time (when the Greenwich 
hours exceed 12, take out for midnight same day, and for noon 
of next day), the difference in each case is the change in 12 
hours, which multiplied by the remaining hours and tenths of 
an hour of the Greenwich time, and divided by 12, gives the 
correction to be added to the semi-diameter, and horizontal 
parallax as taken from the almanac, if increasing; but sub 
tracted if decreasing. We now have the reduced semi-diame¬ 
ter and horizontal parallax. 

6. From Table 18, Bowditch, or Table D, Norie, take out 
the augmentation, which add to the reduced semi-diameter, 
and we have the correct semi-diameter. 

7. From Table 19, Bowditch, or Table E, Norie, take 01 U 
the correction for latitude, which subtract from the reduced 
horizontal parallax. 









MOON’S MERIDIAN ALTITUDE 


111 


EXAMPLE.—1902, March 17th 4h 17 m 36 s M. T. G.; 
Lat. 39° N., Alt. 52° 31'. Required, the moon’s semi-diameter 
and horizontal parallax. 


M. T. G. Mar. I7d 4h 17m 36s 


S. dja. 17th, noon... . 16’ 04” .4 
S. dia. 17th, midnight 16 .01 .4 


3 

4-3 



12) 12.9 

Corr. 

~ L75 

S. dia. noon. ... 

.. 16 .4 .4 

Red. S. dia. 


Aug . .. 

.. -b 13 .1 

Aug. Sem. dia. . 

.. 16’ 16” 


4 _ -3 

H. Par. 17th, noon.... 58’ 53” .4 
H. Par. 17th, midnight 58 42 .6 
.10 .8 

•4 .3 

3H 

_ 43 2 

I2 > 46 44 
Corr. — 3 .87 

H. Par. Noon_ 58 .53.4 

Red. H. Par. 58 .49 .5 

Lat. 39 0 N. —_4^5 

Corr. Har. Par. 58’ 45” 


S. Correct the observed altitude for index error if any, 
subtract the dip, add the augmented semi-diameter for a lower 
limb observation, subtract for an upper limb; apply the cor 
rection from Table 24 Bowditch or Table 30 Norie (always add; 
and the result is the true altitude. 


9. Subtract the true altitude from 90° to get the zenith 
distance. Apply the corrected declination as in sun’s meridian 
altitude question, and the result is the latitude. 


FULL EXAMPLE. 

1902, February 26th, A. M. at ship; Long. 121° 03' E.; 
observed meridian altitude of moon’s upper limb was 49° 04' 
30" bearing south, index error -30", eye 28 feet. Find the 
latitude. 


Moon’s Upper Transit 

Long. E. 
121 0 03’ 


or Mer. Pass. 25th 14I1 48m .3 

Retard. 45m .4 

or Mer. Pass. 24 14 02 .9 

4 

Long, time 8 .1 

Retardation- 45 -4 

6,0) 48,4 12 

454 


8 04 12 

3632 


.2 

( 4)367 -74 
24 /6) 91 .93 


Corr.... 15 .32 


Mer. Pass. 

25th I4h 48m 

.3 

Alt. 

.• 49 ° S. 

Corr. — 


15 

•3 


90 

Mer. Pass. Ship 

25 

14 33 


Z. D. 

41 N. 

Long. E 


8 04 

.2 

Decl. 

7 S. 

Mean Time Green 25 

6 28 

.8 

Approx. Lat. 

34 ° N. 


6 .5 
































120 


SELF-INSTRUCTOR IN NAVIGATION 


Decl. 25d 6h = 7 ° 28’ 12” .1 S. incr. 

Corr. +_ 4 40 

Red. Decl. 7 .32 - 5 2 


Var. in 1 Min. 
9 ” - 7 i 
28 .8 

7768 

7768 

i?42_ 

6,0)27,9 648 
Corr. 4.40 


Sem. dia. 25th, noon. 15’ 12” .2 

Sem. dia. 25th, midnight, jr 5_7_.6 

4 .6 

230 
276 
12 ) 29.90 

— 2.49 


Sem. dia. noon_ _ 15 12.2 

Red. S. dia. 15 9.71 

Aug. H- IX -4 

Corr. S. dia. 15 21.11 


Hor. Par. noon. 55’ 42" .0 

Hor. Par. midnight.. 55 24 .9 

17 .r 

.J 

85 5 

1026 

12 ) in . rg 


— 9.26 

Hor. Par. noon. 55 42 .oc 

Red. Hor. Par. 55 32 .74 

Aug. — 3- 4 

Corr. Hor. Par. 55^29 .34 


Obs. Alt. U. L. 

. 49 q 

f 04’ 

30” s. 

Index Err. 



30 


49 

04 

00 

Dip. 


5 

11 


48 

58 

49 

Aug. S. dia. 


15 

21 


48 

43 

28 

Corr. 

. + 

35 

47 

True Alt. 

. 49 

19 

15 


90 

0 

0 

Zen. dist. 

. 4 o 

40 

45 N. 

Red. decl. 

. 7 

32 

52 s. 

Latitude. 

. 33 

07 

53 North, 


LONGITUDE PROM EQUAL ALTITUDES 
AT SEA. 

When the sun’s meridian altitude is over 70°, the longi¬ 
tude may be found at the same time as the latitude, with suf¬ 
ficient accuracy for the ordinary purposes of navigation, by 
observing the times at equal altitudes of the sun, about five 
or six minutes before and after noon. The sum of these times 
divided by two and corrected by the equation of time, applied 
as to mean time, will give the time of mean noon at ship as 
shown by the watch. Applying to this time the error of the 











































LONG. FROM EQUAL ALT’S AT SEA 


121 


watch on Greenwich will give Greenwich time at the mean 
noon of the ship, which is the longitude in time. 

EXAMPLE.—September 15th, 1902, latitude by account 
7° 02' N., Long. 125° 10' W., the following times at equal 
altitudes of the sun near noon were observed to determine the 
longitude: 

A. M., Watch, oh 46m 10s 

P. M., “ o 57 20 

2) 1 43 30 

o 51 45 

Kqu. of time applied as to mean time -j- 4 33 

Watch time of ship mean noon o 56 18 

Watch slow on Greenwich 7 24 38 

Greenwich time at ship mean noon 8h 20m 56s = Long. 125 0 14’ \V. 

The sun being most probably the only object employed 
in this way, the equation of equal altitudes, if required, may 
be computed and applied precisely as if the ship had been 
stationary; but as the greatest change in the sun’s declination 
in one hour is about one minute, and the change of latitude is 
generally much greater, the' equation of equal altitudes is 
commonly neglected as relatively unimportant in a method 
w T hich at sea is necessarily but approximate. 

Or, in other words, in latitudes where the sun’s meridian 
altitude is not less than 70°, observe the altitude of the sun 
about five or six minutes before apparent noon, noting the time 
by chronometer. After having observed the meridian altitude 
for latitude (which has nothing to do with the equal altitude 
problem), set the sextant again to the same altitude you had 
on before noon, look at the horizon towards the sun, watch 
carefully for the moment when his limb will appear to touch, 
and again note the time by the same chronometer. To the 
mean of the two chronometer times apply the error to date, 
and we have mean time at Greenwich. Apply the equation of 
time as to mean time to obtain apparent time at Greenwich. 
It must now be plain that as midway between the two obser¬ 
vations was apparent noon, the apparent time at Greenwich, 
converted into longitude, must be the longitude of the ship. 
Greenwich time best, longitude west; Greenwich time least, 
longitude east. 










122 


SELF-INSTRUCTOR IN NAVIGATION 


EXAMPLE— Sept. 15, 1902. 


Chron. time at A. M. obs., 

9h 

17m 

12S 

“ “ P. M. “ 

9 

. 29 . 

IO 

2 ) 

18 

. 46 . 

22 

Mean of chron. times, 

9 < 

. 23 . 

II 

Chron. error slow, 


- 3 

27 

Mean time Green., 

9 • 

26 . 

38 

Equ. of time, 

JLm 

4 • 

33 

App. time Green., 

9 • 

3i 

11 = 


= Longitude, 142° 47’ 45” West. 


REMARKS ON TAKING OBSERVATIONS 
AT SEA. 

Terrestrial Refraction.—The apparent elevations of the 
summits of high land are subject to great variations, depend¬ 
ing upon the particular states of the air. 

The apparent place of the sea horizon differs also with 
different temperatures of the sea and air. When the sea is 
warmer than the air, the horizon appears below its mean 
p’ace as that at which it is seen when the air and water are at 
the same temperature, and the dip taken from the tables is toe 
small; when the sea is colder than the air, the horizon appears 
above its mean place, and then the tabular dip is too great. 
These facts being well known, where great accuracy is re¬ 
quired the following precautions should be taken: 

When the altitude of a heavenly body is above 60°, the 
altitude may be observed with the sextant from the opposite 
point of the horizon, as well as from the horizon directly 
under it. Half the difference of the two readings is the ap¬ 
parent zenith distance of the center. By this means the dip 
and its uncertainties, together with the index error, are re¬ 
moved. When both the altitude and its supplement are thus 
measured, and the altitude (the object not being on the mer¬ 
idian) is in a state of change, the time must be noted at each 
observation; and the resulting zenith distance will correspond 
to the mean f f the times. 

When fog obscures the horizon from the deck, a new 
horizon may often be obtained by taking up a position on +he 
ship as low as possible, or in a small boat. 











REMARKS ON TAKING OBSERVATIONS 123 


When the sun's limbs are indistinct, altitudes of the 
center may be obtained by bisecting the hazy disc upon the 
horizon. 

Height of Waves.—The running of large waves causes the 
horizon to be in continual motion; while the rise and fall of 
the observer, both from the lifting of the ship b$ the waves 
and her rolling, cause the dip to be continually changing. 
For this reason a mean of three or five sights should always 
be taken in rough weather, or in a small vessel. If the alti¬ 
tude be observed above the deck, as in the top, for instance, or 
from a high bridge, the horizon will appear better defined, 
and the variations of the dip caused by the ship’s motion will 
be less sensible; also the difference of the temperature of the 
sea and the air appears to affect the place of the sea horizon 
less as the observer is more elevated. 

From numerous observations made upon the heights, dis¬ 
tances, and velocities of waves, the heights are found to vary 
from 14 to 32 feet. Sir James Ross observed waves of 36 feet 
in height. The distance from crest to crest of such waves is 
from 150 to 340 feet, while their velocity appears to vary 
between 17 and 28 nautical miles per hour. 


FINDING THE DISTANCE FROM AN OBJECT BY TWO 
BEARINGS AND DISTANCE RUN BETWEEN. 

Right under the number of points between the ship's 
course and second bearing and abreast of the difference in 
points between the course and first bearing is found a num¬ 
ber, multiply this by the miles made in the interval, and we 
have the distance from the object in miles at time of second 
bearing. Allowance should be made for current, if any. 

(See table on next page.) 



124 SELF-INSTRUCTOR IN NAVIGATION 


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DISTANCE TABLE, 


Giving the distance at which an object can be seen at sea, 
the height of the object being known, and the height of the 
observer’s eye. 

Enter the table with the height of the eye in feet and 
take out the corresponding distance. Seek also for the dis¬ 
tance corresponding to the height of the object in feet. The 
sum of these distances will equal the distance between the 
observer and the object. 


Height in 
feet. 

Distances. 

Height in 
feet. J 

Distances. 

Height in 
feet. 

Distances. 

Nautical 

Miles. 

Land 

Miles. 

Nautical 

Miles. 

Land 

Miles. 

Nautical 

Miles. 

Land 

Miles. 

5 

2.56 

2.96 

70 

9.60 

11.07 

250 

18.14 

20.92 

10 

3 63 

4.18 

75 

9-93 

11 .46 

3 °° 

19.87 

22.91 

15 

4-44 

512 

80 

10.26 

11 83 

350 

21.46 

24.75 

20 

5 13 

5-92 

85 

10.57 

12.20 

400 

22.94 

26.46 

25 

5-74 

6.61 

90 

10.88 

12.55 

450 

24.33 

28.06 

30 

6 28 

7 24 

95 

11.18 

12.89 

500 

25 65 

29.58 

35 

6.79 

783 

100 

11.47 

13-23 

550 

26.90 

| 3102 

40 

725 

8-37 

IlO 

12.03 

13-87 

600 

28.10 

I 32.40 

45 

7.70 

8.87 

120 

12.56 

14.49 

650 

29.25 

! 33-73 

5 ° 

8.11 

9-35 

130 

13.08 

15.08 

700 

30.28 

35-00 

55 

8.51 

9.81 

140 

13-57 

15-65 

800 

32.45 

! 37.42 

60 

8.89 

10.25 

150 

14.22 

16.20 

900 

34 54 

I 39-*4 

65 

9 25 

10.66 

200 

16.22 

18.71 

1000 

36.28 

1 41-83 


EXAMPLE.—Suppose a lighthouse 250 feet high, and 
the observer’s eye on a steamer’s bridge elevated to 30 feet. 


30 ft. = naut. miles. 6.28 

250 ft. = naut. miles.18.14 


Distance between = 24.42 nautical miles. 


SHIP’S PAPERS. 

All merchant vessels have on board some official docu¬ 
ment, or voucher, to prove her nationality, issued by the au¬ 
thorities of her country. The official voucher of a vessel which 
belongs to a country possessing a register of its mercantile 
marine, is a certificate of her registry; in other cases its form 
varies and is called by different names, simh as “passport,” 
“sea-brief,” etc. 




























126 SEIF INSTRUCTOR IN NAVIGATION 


Certificate of Registry—This is a document signed 
by the registrar of the port to which the vessel belongs, 
and usually specifies the ship’s name and name of the 
port to which she belongs, tonnage, etc; name of her mas¬ 
ter ; particulars of her origin, and the names and descrip¬ 
tion of her registered owners. 

Passport.—This is a requisition on the part of a state 
or sovereign power to allow a vessel to pass freely with 
her company, passengers and merchandise without hind¬ 
rance, seizure, or molestation, as being owned by citizens 
or subjects of such state or soverign power. This usually 
contains the name of the master, the name, description 
and destination of the vessel. 

Sea-Brief.—The sea-brief, or sea-letter, is a document 
issued by the civil authorities of the port from which the 
vessel is fitted out; it entitles the master to sail under the 
flag and pass of his nation; and it specifies the nature and 
quantity of the cargo, its ownership and destination. 

Charter Party.—This is a written contract by which 
a vessel is let in part or in whole* The person hiring is 
called the charterer. It is executed by the owner or mas¬ 
ter, and by the charterer. It usually specifies (with other 
things) the name of the master, name and description of 
the vessel, the port where she was lying at the time of 
the charter, name and residence of the charterer, nature 
of the cargo to be shipped, port of loading, port of de¬ 
livery and the amount of freight to be paid. 

Official Log Book.—This is the log book which the 
master is required to keep in the form prescribed by the 
municipal law of the county to which the ship belongs. 

Ship’s Log Book.—This is usually kept by the mate, 
subject to endorsement by the master! It is kept for the 
information of the owner, and for future reference. If 
properly filled in. it is sometimes very useful in the set¬ 
tling of cases of damage caused by stress of weather, etc. 

Builder’s Contract.—On a vessel which has not 
changed hands since construction, this is usually found 
It is not a necessary document, but it sometimes serves! 
m the absence of the pass or sea-letter or certificate of 
registry, to verify the nationality of a vessel. 

Bill of Sale.—An instrument by which a vessel is trans- 


SHIP’S PAPERS 


127 


ferred to a purchaser. It should be required whenever a sale 
of a vessel is alleged to have been made, either during war or 
just previous to the commencement of a war, and if there is 
any reason to suspect that the vessel is liable to detention, 
either as an enemy’s vessel, or as an American or allied vessel 
trading with the enemy. 

Bill of Lading.—Bills of lading usually accompany each 
lot of freight. The bill of lading on board ship is a duplicate 
of the document given by the master to the shipper of the 
goods or freight shipped. On it are specified the name of the 
shipper, date and place of shipment, name and destination of 
such goods, and the amount of freight to be paid on that par¬ 
ticular lot of goods for which the bill of lading is made out. 

Manifest.—This is a list of the cargo on board. It con¬ 
tains the mark and number of every package, the names of 
shippers and consignees, a specification of the quantity of 
goods in each package, as coffee, sugar, molasses, etc. and an 
account of the freight corresponding with the bills of lading. 
It is usually signed by the ship broker who clears the vessel 
out at the custom house, and by the master. 

The Clearance is the custom house certificate, given at the 
last port from whence the vessel came. It shows that the 
customs duties have been paid, and it specifies the cargo and 
its destination. 

The Crew List, or Muster Roll, contains the name, age, 
rating, place of residence and place of birth of every member 
of the ship’s company. 

Shipping Articles.—The agreement for the hiring of sea 
men. They are signed by all members of the crew, which in¬ 
cludes the various departments, and should describe aecur 
atelv the voyage, and terms under which seamen, or members, 
engage. 

Bill of Health.—This document certifies that the vessel 
comes from a port where no contagious disease prevails, and 
that all of the crew were free from any such contagion at the 
time of her departure. 


128 


SELF-INSTRUCTOR IN NAVIGATION 


ROPE, CHAINS, ETC. 

Practical Rule for Finding the Strength of Hawser-laid 
Rope.—Square the circumference and divide by 3 for the 
breaking strain, in tons; by 4 for the proof strain; by 6 for 
the working strain. 

To Find What Weight a Rope Will Lift When Rove as a 
Tackle.—Multiply the weight the rope is capable of suspend¬ 
ing by the number of parts at the movable block, and subtract 
one-fourth of this for resistance. 

To Ascertain the Relative Strength of Chain and Rope.— 
Consider the proportional strength to be 10 to 1, using the 
diameter of the chain and the circumference of the rope. Half¬ 
inch chain may replace 5-inch rope. 

RELATIVE SIZES OF CHAIN OR WIRE WHICH MAY 
BE SUBSTITUTED FOR HEMPEN ROPE. 


HEMP. 

CHAIN. 

WIRE. 

i HEMP. 

CHAIN. 

WIRE. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches 

3 

T?f 


8 

ft 

3/"2 

4 

H 

I X 

9 

I 

4 

5 

A 

2 

IO 

I ft 

4 ft 

6 

ft 

2 % 

ii 

iX 

5 

7 

H 

3 

1 




















PAINTING SHIP 


129 


COMPARISONS IN WIRE, CHAIN AND ROPE. 


Patent Flexible Steel 
Wire Cables. 

Chain Cable. 

Tarred Hemp 
Rope. 

Circum¬ 

ference. 

Weight 

per 

Fathom. 

Breaking 

Strain. 

Diameter , 

of Sheave 
or Barrel. 

u 

N 

<55 

Weight per 

Fathom. 

Proof 

Strain. 

Breaking 

Strain. 

N 

c n 

Weight 

per 

Fathom. 

Breaking I 

Strain. 1 

Inch’s 

Lbs. 

Tons. 

Inch’s 

Inch’s 

Lbs. 

Tons. 

Tons. 

Inch’s 

Lbs. 

Tons. 

12 

115 

320 

72 








11 

97 

270 

66 








IO 

So 

220 

60 








9 

65 

180 

54 








8 

53 

150 

48 

2-A 

280 

96X 

I34X 

25 

146 

125 

7X 

47 

130 

45 

2 -A 

256 

86 X 

120)^ 

24 

134 

115 

7 , 

4i 

ji6 

42 

2* 

231 

76X 

107* 

23 

123 

106 

6 X 

37 

102 

39 

lit 

204 

6?X 

94 X 

21 

106 

89 

6 

33 

88 

36 

1 i 

166 

55 X 

77 X 

19 

84 

72 

5 % 

28 

74 

33 

1 1 

143 

47 X 

66 X 

17 

67 

60 

5 

23X 

64 

3° 

1 Ar 

112 

37 X 

55 X 

15 

56 

50 

4X 

15 

I 39 

27 

ii 

68 

22 X 

34 X 

13 

39 

34 

4 

12 

i 33 

24 

1 

54 

18 

27 

12 

33 

29 

3X 

9 

1 26 

21 

It 

48 

15 A 

23 t 7 o 

11 

28 

24X 

3 X 

8 

i 22 

I9X 

ft 

35 

11X 

i 7tV 

IO 

23 

20 

3 

7 

! 18 

18 

ft 

30 

10X 

15 X 

9 

19 

16X 


5X 

! 15 

16 X 

f 6 

25 

8X 

I2X 

8X 

16X 

14 


4X 

12 

15 

— 

— 

— 

— 

7X 

13 

11X 

2X 

3X 

9 

13 X 

1 0 
16 

21 

7 

9X 

6X 

11X 

IO 

2 

2X 

7 

12 

— 

— 

— 

— 

5 X 

9 

8 

*X 

2 

5X 

IO X 

16 

17 

5X 

7X 

5 

6X 

6 

I X 

iX 

4 

9 

— 

— 

— 

— 

4 

4 

4 

iX 

I 

2 X 

7 X 

i 

14 

4X 

6 

3X 

3 

2X 

I 

xl 

1X 

6 


— 

— 

— 

2X 

2 

IX 


If the rope only passes over a sheave, the diameter of the 
sheave may be one-sixth less than if it passed completely 
round a barrel, but in every case, the diameter of either sheave 
or barrel should be as large as practicable. 


PAINTING SHIP. 

In all ordinary colors white lead is the principal ingredi¬ 
ent. A good quality should be obtained, as cheap lead con¬ 
tains “byrates,” which kills the body of it, and makes it less 
proof against the weather. White lead improves by keeping. 
The oil and turpentine used in mixing should be thoroughly 
incorporated with the lead. Half an ounce of patent dryers 
is the proportion to one pound of color. 

Zinc white is said to be more durable than white lead, 
although it has less body. It is very pure. 








































130 


SELF-INSTRUCTOR IN NAVIGATION 


Vegetable black is a cheap and good black for ordinary 
purposes. When dry it resembles soot, and being free from 
grit does not require grinding. It should always be mixed 
with boiled oil. 

Vermilion, while in a powder, can be tested by placing a 
dust of it on clean white paper, and crushing it with the thumb 
nail. If pure, it will not change color by rubbing; but if 
adulterated, it will become a deep chrome yellow, or assume 
the appearance of red lead, showing the stuff used in its adul¬ 
teration. This accounts for the unstable quality of inferior 
vermilion. If two coats are necessary, both must be of the 
best quality to insure success. 

The most serviceable blue is French ultramarine. It is a 
permanent, kindly working color, and affords a variety of clear 
tints when mixed with white. It is a brilliant blue, and pre¬ 
serves its purity when reduced in tone by the addition of 
white. It may be deepened by Russian blue or indigo, or by 
a trifling addition of vegetable black. 

Green, like black, must be mixed with boiled oil, or boiled 
oil and varnish; and not with linseed oil and turpentine. 

The allowance of paint for well regulated vessels is based 
on the calculation that all weather work outside and inside 
has one coat every four months; and between decks one coat 
every twelve months. This is considered to give paint enough 
for boats, etc. 

One pound of stiff white paint with the necessary thin¬ 
nings, is supposed to cover about five and one-half square 
yards of smooth surface. The same quantity of black about 
eight square yards. 


PROPORTIONS FOR MIXING. 


PROPORTIONS 

FOR 

BLACK. 

WHITE 

RAW 

LINSEED 

OIL. 

BOILED 

LINSEED 

OIL. 

turpen¬ 

tine. 

lith¬ 

arge. 

Outside. 

lbs. 

IOO 

lbs. 

Gals. 

3 X 

2 

Gals. 

*X 

Gals. 

X 

X 

x 

Gals, 

5'A 

3X 

3X 

3X 

Outside. 

IOO 

Upper deck— 
Weather deck 


IOO 


Between dks— 
Cabins, Boats,etc. 


IOO 

.iX_ 


IX 






















PAINTING SHIP 


131 


Litharge should always be ground in oil, and on no ac¬ 
count must it be put in paint in a dry state. It should not be 
mixed in paint until it is about to be used. 

MIXING COLORS. 

Cream Color.—Crome yellow, the best Venetian red and 
w T hite lead. 

Fawn Color.—Burnt sienna^ ground very fine, mixed with 
white lead. 

Drab.—Raw or burnt umber and white lead, with a little 
Venetian red. 

Purple.—White lead, Prussian blue and vermilion. 

Violet.—White lead, French ultramarine, vermilion, and 
a very little black. 

French Gray.—White lead and Prussian blue, tinged with 
vermilion. 

Salmon Color.—White lead, tinged with the best Venetian 

red. 

Imitation of Gold.—Mix white lead, chrome yellow and 
burnt sienna until the proper shade is obtained. 

USEFUL RECIPES. 

A good coating for Tarpaulins.—Add twelve ounces of 
beeswax to one gallon of linseed oil; boil two hours; prime 
the cloth with this mixture, and use it instead of boiled oil 
for mixing the coating. 

Copper Color Paint.—Six parts of spruce ochre, one part 
of Venetian red and one part of black. 

Bronze Paint.—Chrome green, two pounds; ivory black, 
one ounce; chrome yellow, one ounce; good Japan, one gill. 
Grind all together and mix with linseed oil. 

Removing Old Paint.—Nothing is so efficacious as heat, 
applied by a small brazier with a handle. 

One part of pearl ash mixed with three parts of quick 
stone lime (slacking the lime in water and then adding pearl 
ash), laid over paint work, and allowed to stand fourteen to 
sixteen hours, will so soften it, that it can be easily scraped off. 

Putty.— Well dried and sifted whiting, 100 pounds, and 


132 


SELF-INSTRUCTOR IN NAVIGATION 


one and three-fourths gallons of linseed oil well mixed, left 
for three days, and then worked up again before using. 

Spar Varnish.—Boiled oil and resin. 

Marine Glue.—One part india-rubber, twelve parts min¬ 
eral naphtha; heat gently, mix and add twenty parts of pow¬ 
dered shellac. Pour out on a slab to cool; when used to be 
heated to about 250° Fahr. 

Glue to Resist Moisture.—Glue which has been swelled by 
water dissolved in linseed oil. 

Glue Cement to Resist Moisture.—One pound glue, one 
pound black resin, quarter pound red ochre, mixed with the 
least possible quantity of water. 

Cement for Cloth or Leather.—Sixteen pounds of gutta¬ 
percha cut small, four pounds india-rubber, two pounds pitch, 
one pound shellac, two pounds linseed oil, melted together 
and well mixed. 

Waterproofing for Boots.—One quart linseed oil, six 
ounces of beeswax, four ounces spirits of turpentine, one 
ounce Burgundy pitch. Melt wax and oil together and dis¬ 
solve the pitch in the turpentine, pour both into a jar, and 
place it in a saucepan with water, boil and stir till well mixed. 
Being very inflammable. bew T are of fire getting near it. 

Yellow for Smokestacks.—Whiting 37 pounds, yellow 
ochre 74 pounds, glue 6 pounds. The glue is made into size 
and added hot to the whiting, etc., mixed with water enough 
to give the proper consistency for use. 

White.—Whiting 37 pounds, glue f> pounds. 

French Polish.—Five ounces of naphtha, one ounce of 
shellac, one dram of myrrh, ten grains of isinglass and six 
Irams of olive oil. 


FLAGS AND PENNANTS 


133 


INTERNATIONAL CODE FLAGS AND PENNANTS. 

A = White and Blue Swallow-tail. 

B — Red Swallow-tail. 

C — White pennant with red ball. 

D = Blue pennant with white ball. 

E — Red white and blue pennant. 

F = Red pennant with white cross. 

G — Yellow and blue pennant. 

H = White and red square. 

I — Yellow square with blackball. 

J — Blue white and blue, horizontal, square flag. 

K — Yellow and blue square. 

L — Yellow and black in 4 squares. 

M — Blue square with white diagonal cross. 

N = Blue and white in 16 squares. 

0 — Yellow and red, separated diagonally, square flag. 
P = Blue square with white square in center. 

Q = Yellow square. 

R = Red square with yellow cross. 

S — White square with blue square in center. 

T — Red white and blue, vertically, square flag. 

U = Red and white in 4 squares. 

V — White square with red diagonal cross. 

W — Blue white and red square, border blue, center red. 
X — White square with blue cross. 

Y = Yellow and red diagonal stripes, square flag. 

Z = Black, yellow, blue and red, in 4 triangles, forming 
a square. 

The “Code Flag” and or “Answering Pennant” 
is a pennant with red and white vertical stripes. 

When used as the “Code Flag” it is to be hoisted 
under the Ensign. 

When used as the “Answering Pennant” it is to be 
hoisted at the mast head or where best seen. 


134 SELF INSTRUCTOR IN NAVIGATION 


GENERAL RULES FOR SIGNALING BY THE IN¬ 
TERNATIONAL CODE FLAGS. 

Ship A wishing to signal, hoists her Ensign with the 
Code Flag under it., 

Ship B answers by hoisting her Answering Pennant 
at the “Dip,” that is about two thirds up. 

Ship A now makes the signal desired, first hauling 
down her Code Flag if required to make the signal. 

When A’s signal is understood by B and found in 
the Signal Book, B hoists her Answering Pennant “Close 
Up,” and keeps it there until A hauls down. 

B then lowers her Answering Pennant to the “Dip” 
and waits for the next signal from A; and so on. 

Each hoist that A makes should be kept flying until 
B answers with her Answering Pennant “Close Up.” 

"When A has finished signaling, she hauls down her 
Ensign, and the Code Flag if not already down. 

The Answering Pennant should be hoisted where 
best seen. 

Signal Flags should always be hoisted where they 
can best be seen; not necessarily at the mast head. 

To make a signal, look for the principle word in the 
communication you wish to make (pages 143-451), in the 
Signal Book, and there find the Code Flag letters of the 
flags to be hoisted. 

To interpret or decipher a signal made, find the flag 
letters in alphabetical order in the Signal Book, and be¬ 
side these will be found the meaning of the signal. 

Urgent and important signals are Two flag signals . 

General signals are Three flag signals. 

Geographical, alphabetical spelling tables, and ves¬ 
sel J s numbers are Four flag signals. 

The Signal Book has Three Parts, namely: 

1st part, Urgent and Important; 

2nd part, General Index, arranged alphabetically; 

3rd part, Lists of U. S. Storm-warning, Life-saving 
and Wireless Stations, Etc. 


NEW INTERNATIONAL CODE FLAGS. 


CODE FLAG” AND “ANSWERING PENDANT.” 


When used as the “ Code Flag” 
it is to be hoisted under the 
ensign. 



When used as the “ An¬ 
swering Pendant ” it is to be 
hoisted at the mast-head or 
where best seen. 


•LK 

frb^_ 

G 

► 1 

B | 

Qu 

V 

JARANTI N£ 

IX 

M 

h 

U-P 

I •( 

gg - 


c 

1 

I* 

i •[ 

□ X 

ffi 


J 

g o| 

3 

□ 

!P 

K 

u 

Blue 

3 i 

Peter 

S 

M 


C 




Assent - Yes —' 


Negative - No 


Powder Flag 


• ■ 

Cholera Yellow Fevor 



About to Proceed 
to Sea 



I Require A Pilot 


NOTE—From January 1, 1902, the use of the New International Code Flags is 
compulsory and they only will be recognized. 















































































































\ 













*■ 














* 








/ 


r 








1 

i 

i 

t 



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i 




























FOGOMETER 


135 


DESCRIPTION AND USE OF THE FOGOMETER, 
WITH ACCOMPANYING DIAGRAM, AND DIS¬ 
TANCE TABLES FOR READY REFERENCE 


Patented July 12, 1910 by W. J. Smith, Master Mariner, President The 

Seattle Nautical School, 507 Maritime Building, Seattle, Wash. 

This is an instrument for facilitating the process of ac¬ 
curately determining a ship’s position (both as to the bearing 
of, and the distance from a light-house, etc.) in foggy weather, 
by the use of wireless telegraph and sound waves, when within 
hearing distance of a wireless shore station, the ship having a 
wireless outfit. 

It is well known that sound in air travels 1123 feet per 
second, at a temperature of 60 deg. Fahr. This may be used for 
all practical purposes. Wireless waves however travel with the 
speed of light, i. e. 186,330 miles per second. The velocity of 
sound in sea water is 4593 feet per second. 

If a wireless station sends a “wireless’ simultaneously 
with the regular sound signal used during fog, the time in¬ 
terval in seconds between tick of wireless instrument on board 
and the moment when the sound signal reaches the ear, mul¬ 
tiplied by 1123, and the result divided by 6080 (feet in a naut. 
mile), will equal the distance off, and the ship will be some¬ 
where on the arc of a circle at that distance from the shore 
station. Now, if the ship be run on her course for a certain 
distance by log, and her distance off again found by wireless 
and sound as above, she will again be somewhere on the arc 
of a circle at that (the second found) distance off. It will 
now be seen that we have the three sides of a triangle, and if 
we take the course with the parallel rule and the distance run 
in the interval with the dividers, and slide the former towards 
the shore station on the chart until the two legs of the dividers 
will just fall on the two arcs already described, the ship's posi¬ 
tion at time of both first and second observations will be des¬ 
ignated by these two points thus found. These results can 
be readily verified by a simple caluculation of trigonometry. 

All this seems like making a drawing board of the chart, 
but the Fogometer obviates the necessity of marking and 



136 SELF INSTRUCTOR IN NAVIGATION 


erasing pencil lines; and provides means whereby the forego¬ 
ing results are obtainable in a most convenient and rapid man¬ 
ner, and with a nice degree of accuracy. 

Should the vessel be within the range of a submarine fog 
signal station, also equipped with wireless apparatus, the time 
interval in seconds between tick of wireless and submarine 
sound received on board, multiplied by 4593, and the result 
divided by 6080, will give the distance off; and her position 
can be found by the method already described. 

The accompanying tables, which are selfexplanatory, will 
at once give the distance off by inspection, when the time in¬ 
terval in seconds has been noted. 

To Use the Fogometer. 

Lay the instrument flat upon the chart with its side A 
off-shore and the arms B and C directed inshore towards the 
light-house, and crossed. Set the sliding block on side A to 
the run the ship has made between the observations and clamp 
it, and adjust the arms B and C to their respective distances 
off ; then make all rigid by means of the thumb screws. The 
intersection of B and C is now positioned over the light-house 
L H as a pivotal point, and the instrument slued so as to make 
the offshore side A conform to the edge of the parallel rule cor¬ 
responding to the ship’s course. A pencil point should now 
be inserted in the apertures for the purpose, to mark the chart. 
The correct bearing of, and distance from the light-house are 
now assured, using the chart scale for the distance instead of 
the scale of the instrument. 

It would be needless to attempt to graduate the instru¬ 
ment to suit the various scales on which charts are projected; 
and the average man will readily see that this, even if it were 
practicable, is unnecessary. The bearing of the shore object 
will be the same, no matter what scale is used. The scale, one 
half inch to the nautical mile has been adopted as sufficiently 
large to insure accurate proiection on any coast chart. We as¬ 
sume that the graduations are nautical miles, subdivided into 
tenths, and use the instrument as directed. The ship will be 
on a line passing through the spot which marks the end of 


130 



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TABLE I. 

Distance of ship from Wireless Station, when time interval in seconds between receipt of wireless 
and air sound signals, dispatched simultaneously, has been noted on board._ 


Secs. 

interval. 

Dist. off 
Wireless 
Station. 

Secs. 

interval. 

Dist. off 

Wireless 

Station. 

Secs. 

interval 

Dist. off 

Wireless 

Station. 

Secs. 

interval. 

Dist. off 

Wireless 

Station. 

Secs. 

interval. 

Dist. off 
Wireless 
Station. 

Secs. 

interval 

Dist. off 
Wireless 
Station. 


Naut. 

miles. 

s 

Naut. 

miles. 

s 

Naut. 

miles. 

s 

Naut. 

miles. 

s 

Naut. 

miles.* 

s 

Naut. 

miles. 

1 

.18 

11 

2.03 

21 

3.88 

31 

5.73 

41 

7.57 

51 

9.42 

2 

.37 

12 

2.22 

22 

4.06 

32 

5.91 

42 

7.76 

52 

9.60 

3 

.55 

13 

2.40 

23 

4.25 

33 

6.10 

43 

7.94 

53 

9.79 

4 

.74 

14 

2.59 

24 

4.43 

34 

6.28 

44 

8.13 

54 

9.97 

5 

.92 

15 

2.77 

25 

4.62 

35 

6.46 

45 

8.31 

55 

10.16 

6 

1.11 

16 

2.96 

26 

4.80 

36 

6.65 

46 

8.50 

56 

10.34 

7 

1.29 

17 

3.14 

27 

4.99 

37 

6.83 

47 

8.68 

57 

10.53 

8 

1.48 

18 

3.32 

28 

5.17 

38 

7.02 

48 

8.87 

58 

10.71 

9 

1.66 

19 

3.51 

29 

5.36 

39 

7.20 

49 

9.05 

59 

10.90 

10 

1.85 

20 

3.69 

30 

5.54 

40 

7.39 

50 

9.24 

60 

11.08 


DEFINITION. 

Sound travels 1123 feet per second in air at a temperature of 60° Fahr. This may be used for all 
practical purposes. Wireless travels with the speed of light, 186,330 miles per second. Distance 
off=sees. interval between tick of instrument and sound of shore signal XH23-f-6080. 

TABLE II. 


Distance of ship from Wireless Station, when time interval in seconds between receipt of wireless 
and submarine sound signals, dispatched simultaneously, has been noted on board. 


Secs. 

interval. 

Dist. off in 

Naut. miles. 

Secs. 

interval. 

Dist. off in 

Naut. miles. 

Secs. 

interval. 

Dist. off in 

Naut. miles. 

Secs. 

interval. 

Dist. off in 
Naut. miles. 

1 

.76 

6 

4.53 

11 

8.31 

16 

12.09 

2 

1.51 

7 

5.29 

12 

9.07 

17 

12.84 

3 

2.27 

8 

6.04 

13 

9.82 

18 

13.60 

4 

3.02 

9 

6.77 

14 

10.58 

19 

14.35 

5 

3.78 

10 

7.55 

15 

11.33 

20 

15.11 




DEFINITION. 




Sound in sea water 

travels 4593 feet per second. Distance off =seeonds interval between tick of 

instrument and sound of submarine 

signal X4593-7-6080. 







TABLE III. 




Distance of ship from that part of the land (etc.) 

from whence an echo 

is returned, 

when the time 

interval 

in seconds between sound of whistle (ship’s 

gun, etc.) and return of echo has been noted. 

Secs. 

Dist. off in 

Secs. 

Dist. off in 

Secs. 

Dist. off in 

Secs. 

Dist. off in 

interval. 

Naut. miles. 

interval. 

Naut. miles. 

interval. 

Naut. miles. 

interval. 

Naut. miles. 

1 

.09 

16 

1.48 

31 

2.86 

46 

4.25' 

2 

.18 

17 

1.57 

32 

2.96 

47 

4.34 

3 

.28 

18 

1.66 

33 

3.05 

48 

4.43 

4 

.37 

19 

1.75 

34 

3.14 

49 

4.53 

5 

.46 

20' 

1.85 

35 

3.23 

50 

4.62 

f> 

.56 

21 

1.94 

36 

3.32 

51 

4.71 

7 

.65 

22 

2.03 

37 

3.42 

52 

4.80 

8 

.74 

23 

2.12 

38 

3.51 

53 

4.89 

9 

.83 

24 

2.22 

39 

3.60 

54 

4.99 

10 

m 

25 

2^31 

40 

3.69 

55 

5.08 

11 

1.02 

26 

2.40 

41 

3.79 

56 

5.17 

12 

1.11 

27 

2.49 

42 

3.88 

57 

5.26 

13 

1.20 

28 

2.59 

43 

3.97 

58 

5.36 

14 

1.29 

29 

2.68 

44 

4.06 

59 

5.45 

15 

1.39 

30 

2.77 

45 

4.16 

60 

5.54 


definition! “ — 

As sound travels 1123 feet per second, and 6080 feet equal one nautical mile: Then dist, off 
— (secs, interval between sound and echoX1123-4-2) -4-6080. 






















FOGOMETER 


137 


the run, and the light-house, and her distance off on that line 
will be found by using the chart scale, and distance determined 
at second observation. If the chart scale is larger than that 
of the instrument she will be outside the marked spot on a 
projection of the line, but inside if the chart scale is smaller. 

For Example: 

A steamer is approaching the Strait of Juan de Fuca from 
the southward in a dense fog. Fie is within hearing distance 
of Tatoosh (Cape Flattery) wireless station but uncertain of 
it correct bearing and distance away. He calls the light house 
by wireless and requests the operator to dispatch wireless and 
sound waves simultaneously, and to repeat the dual signal in 
say thirty minutes. The wireless instrument is now closely 
watched and the sound signal listened for, and the time interval 
between the signals received as noted is say 41% seconds. 
Reference to'Table I. shows the distance off to be 7.7 miles 
(naut.). Thirty minutes later, the interval between wireless 
and sound as noted on board is say 27% seconds, for which 
interval the same table gives 5.1 miles. During the interval 
between the observations, the ship steaming 11 knots per hour 
has covered 5% miles of distance on a course N. 10 cleg. W. 
magnetic. The accompanying diagram will show the case in 
hand. Now set the sliding block on side A of the instrument to 
the ship’s run 5% miles and clamp it, and adjust the arms B 
and C to correspond to the distances off obtained, 7. e. 7.7 and 
5.1 respectively, and make all rigid by the thumb screws. The 
instrument is laid upon the chart with side A offshore and the 
intersection of B and C positioned over the light house. Slue 
the instrument till side A conforms to the edge of the parallel 
rule containing the course, and mark the chart with a pencil 
point through the aperture at the end of the run. The ship 
is now on the line passing through this mark and the light¬ 
house, and her actual distance off can be measured by the chart 
scale, while the parallel rule and the compass rose on the chart 
will give the correct bearing of the light-house. Arms B and 
C and be used interchangably to suit the ship’s course along 
the coast either way. 


138 SELF INSTRUCTOR IN NAVIGATION 


Shore stations may be called upon to despatch sound and 
wireless waves simultaneously at intervals as desired; and it 
is highly probable that in the near future it will become an 
established custom for these stations to send such simul¬ 
taneous dispatches at stated intervals during fog, as an addi¬ 
tional aid to navigation. 


RULE FOR LONGITUDE BY SUNRISE OR SUNSET. 

Get the Mean Time at Greenwich and correct the De¬ 
clination and Equat ion of Time, and find the Polar Dis¬ 
tance, as usual. 

To the Dip for height of the eye add the Refraction 
for 0 deg. Altitude; then add the Semidia. and subtract 
the Parallax in the case of an Upper Limb, but subtract 
both Semidia. and Parallax for a Lower Limb observa¬ 
tion. The result in either case is the Negative Altitude. 

Add together the Latitude and Polar Distance, and 
from the sum subtract the Negative Altitude; divide what 
remains by 2 for the Half Sum, and to the Half Sum add 
the Negative Altitude, and thus obtain the Remainder. 
Now proceed in the usual way for the Hour Angle, and 
thence the Longitude. 



CONTENTS _ 

Mariner’s Compass. 3 

Logarithms. 5 

Parallel Sailing. 12 

Days Work. 13 

Latitude by Meridian Altitude. 21 

Mercator’s Sailing. 26 

Amplitude. 29 

Longitude by Chronometer. 35 

Time Problems. 42 

Compass Error by Azimuth. 44 

Time Azimuth. 50 

Reduction to Meridian. 53 

Latitude by Star. 58 

Latitude by Polaris. 59 

Longitude by Star. 63 

Position by Sumner. 65 

Sumner Chart. 69 

Johnson’s Double Altitudes. 71 

Star Time Azimuth. 75 

On the Chart. 77 

Great Circle Sailing. 80 

Chartlet . 81 

Current Sailing. 81 

Definitions . 82 

Adjustments of the Sextant. 86 

The Log Line. 88 

The Lead Line. 89 

Distances off Lighthouses. 89 

Sound and Echoes. 91 

Uniform System of Buoyage. 92 

Nautical Almanac Elements. 93 

Mean Places of Stars. 99 

Answers. 99 

Beaufort Notation. 103 

Rule of the Road. 104 

Aids to Memory, in Verse. 115 

Moon’s Meridian Altitude. 117 

Longitude from Equal Altitudes at Sea. 121 

Remarks on Taking Observations. 122 

Distance Table. 125 

Ship’s Papers. 125 

Rope, Chains, Etc. 128 

Painting Ship. 129 

New International Code Flags and Pennants. 133 

Rules for Signaling by International Code Flags. 134 

Description and Use of the Fogometer. 135 

Rules for Longitude by Sunrise or Sunset. 138 

















































AUG 19 1912 













































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